Please select the eligibility criteria that correspond to the clinical trial below.
Title: A Phase III Randomized Controlled Clinical Trial of Carboplatin and Paclitaxel (or Gemcitabine) Alone or in Combination With Bevacizumab (NSC #704865) Followed by Bevacizumab and Secondary Cytoreductive Surgery in Platinum-Sensitive, Recurrent Ovarian, Peritoneal Primary and Fallopian Tube Cancer. NCI-Supplied Agents: Bevacizumab (NSC #704865)
Brief Summary: This randomized phase III trial studies carboplatin, paclitaxel and gemcitabine hydrochloride when given together with or without bevacizumab after surgery to see how well it works in treating patients with ovarian, epithelial, primary peritoneal, or fallopian tube cancer that has come back. Drugs used in chemotherapy, such as carboplatin, paclitaxel and gemcitabine hydrochloride work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Immunotherapy with monoclonal antibodies, such as bevacizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. It is not yet known whether combination chemotherapy is more effective when given with or without bevacizumab after surgery in treating patients with ovarian, epithelial, primary peritoneal, or fallopian tube cancer.


Options:
A: Inclusion Criteria:

* Diagnosis of ovarian epithelial, primary peritoneal, or fallopian tube cancer
* Recurrent disease
* Must have received a prior platinum-based regimen
* Platinum-sensitive (treatment-free interval \> 6 months)
* No more than 2 prior chemotherapy regimens
* Measurable disease
* At least 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques OR \>= 10 mm by spiral CT scan
* Not in a prior irradiation field
* No known brain metastases
* Performance status:

  * ECOG 0-2 OR
  * Karnofsky 80-100%
* Life expectancy:

  * More than 12 weeks
* Hematopoietic:

  * Absolute neutrophil count \>= 1,500/mm3
  * Platelet count \>= 100,000/mm3
  * Hemoglobin \>= 9 g/dL
  * No bleeding diathesis
* Hepatic:

  * Bilirubin \< 1.5 times upper limit of normal (ULN)
  * AST or ALT =\< 2 times ULN
* No history of allergic reaction attributed to compounds of similar chemical or biological composition to sorafenib or other agents used in the study
* Patients who have had a reaction to a taxane or a platinum and have not yet been rechallenged may undergo a desensitization regimen on study
* No hypersensitivity to paclitaxel or drugs using the vehicle Cremophor El:
* Prior hypersensitivity reaction to paclitaxel allowed provided rechallenged successfully
* Renal:

  * Creatinine \< 2 mg/dL
* Cardiovascular:

  * Abnormal cardiac conduction (e.g., bundle branch block or heart block) allowed if stable for the past 6 months
  * No symptomatic congestive heart failure
  * No uncontrolled hypertension
  * No cardiac arrhythmia
  * No unstable angina pectoris;
  * No myocardial infarction within the past 6 months
* Negative pregnancy test
* Fertile patients must use effective contraception
* Adequate intestinal function
* No concurrent requirements for IV hydration or nutritional support
* No active or ongoing infection
* No psychiatric illness or social situation that would preclude study compliance
* No other concurrent uncontrolled illness
* No other invasive malignancy with the past 5 years except nonmelanoma skin cancer
* More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) and recovered
* More than 3 weeks since prior hormonal therapy
* More than 4 weeks since prior radiotherapy and recovered
* No prior sorafenib
* No prior anticancer therapy that contraindicates study therapy
* No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, or phenobarbital), rifampin, or Hypericum perforatum (St. John's wort)
* No concurrent combination antiretroviral therapy for HIV-positive patients
* No concurrent therapeutic anticoagulation therapy
* Concurrent prophylactic low-dose warfarin allowed for maintenance of venous or arterial access devices
* No other concurrent anticancer therapies
* No other concurrent investigational agents
* Not pregnant or nursing
B: Inclusion Criteria:

* Patients must have the psychological ability and general health that permits completion of the study requirements and required follow up
* Administration of study drugs (pegylated liposomal doxorubicin, bevacizumab, atezolizumab) may have an adverse effect on pregnancy and poses a risk to the human fetus, including embryo-lethality; women of child-bearing potential (WOCBP) must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 5 months (150 days) after the last dose of study agent; should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. (06/29/2017)
* Submission of tumor tissue is required for all patients; investigators should check with their site pathology department regarding release of biospecimens before approaching patients about participation in the trial
* High grade ovarian cancer, including high grade serous; clear cell; endometrioid, grade 3; and others (adenocarcinoma, not otherwise specified \[NOS\]; mixed epithelial carcinoma; undifferentiated carcinoma); NOTE: low grade serous, mucinous and carcinosarcoma histologies are excluded due to their different underlying genomic features and/or clinical behavior; ovarian cancer = ovarian, fallopian tube or primary peritoneal cancer; required data element: submission of pathology report
* Recurrent, platinum resistant ovarian cancer (defined as progression within \< 6 months from completion of platinum based therapy; the date should be calculated from the last administered dose of platinum therapy)
* 1-2 prior regimens (including primary therapy); hormonal therapies (e.g., tamoxifen, aromatase inhibitors) will not count toward the prior regimen limit; PARP inhibitors given in the maintenance setting post response to platinum-based therapy will not count as a separate regimen from the preceding platinum-based therapy. (30-OCT-2020)
* Measurable disease (defined by RECIST v1.1) or evaluable disease (defined as solid and/or cystic abnormalities on radiographic imaging that do not meet RECIST 1.1 definitions for target lesions OR ascites and/or pleural effusion that has been pathologically demonstrated to be disease related in the setting of cancer antigen \[CA\] 125 \>= 2 x upper limit of normal \[ULN\])
* Age \>= 18
* Performance status 0, 1 or 2
* Absolute neutrophil count (ANC) \>= 1,500/mcl (within 14 days prior to registration)
* Platelets \>= 100,000/mcl (within 14 days prior to registration)
* Hemoglobin (Hgb) \>= 8 g/dl (within 14 days prior to registration)
* Creatinine =\< 1.5 x institutional upper limit of normal (ULN) (within 14 days prior to registration)
* Urine protein creatinine (UPC) ratio must be \< 1.0 (within 14 days prior to registration); if UPC ratio \>= 1, collection of 24-hour urine measurement of urine protein is recommended (24-hour urine protein level must be \< 1000 mg for patient enrollment); If UPC ratio cannot be calculated because the urine protein is below the lower limit of detection of the assay this will not exclude the patient (10/22/2018) (30-OCT-2020); UPC ratio of spot urine is an estimation of the 24-hour urine protein excretion - a UPC ratio of 1 is roughly equivalent to a 24-hour urine protein of 1 gm
* Total bilirubin =\< 1.5 x ULN (patients with known Gilbert disease who have serum bilirubin level =\< 3 x ULN may be enrolled) (within 14 days prior to registration)
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 x ULN (AST and/or ALT =\< 5 x ULN for patients with liver involvement) (within 14 days prior to registration)
* International normalized ratio (INR) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN (or on stable dose of therapeutic anticoagulation, such as low-molecular-weight heparin, warfarin or rivaroxaban) (10/16/2017)
* Thyroid-stimulating hormone (TSH) within normal limits (Euthyroid patients on thyroid replacement therapy allowed provided TSH \< ULN) (02/20/2019)
* The patient or legally authorized representative must provide study-specific informed consent prior to study entry and, for patients treated in the United States (U.S.), authorization permitting release of personal health information

Exclusion Criteria:

* Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation
* Patients who have had systemic anticancer therapy (e.g., chemotherapy, targeted therapy including PARP inhibitors or bevacizumab) within 3 weeks prior to entering the study (30-OCT-2020)
* Patients who have had hormonal therapy (e.g., tamoxifen, aromatase inhibitor) within 1 week prior to entering the study
* Patients with prior treatment with anti-programmed cell death (PD)-1, anti- programmed cell death ligand (PD-L)1 or anti-cytotoxic T-lymphocyte-associated protein (CTLA)-4 therapeutic antibody or other similar agents (10/16/2017)
* Patients with prior treatment with bevacizumab (or any other anti vascular therapy, e.g., cediranib) for platinum resistant recurrence; (Note: prior bevacizumab in initial therapy and/or platinum sensitive recurrent setting is allowed) (10/16/2017)
* Patients with prior treatment with PLD
* Prior radiotherapy to the abdomen or pelvis
* Patients who have not recovered from adverse events to =\< grade 1 (other than alopecia) due to agents administered more than 3 weeks earlier (10/16/2017); however, the following therapies are allowed:

  * Hormone replacement therapy or oral contraceptives
  * Herbal therapy \> 1 week prior to cycle 1, day 1 (herbal therapy intended as anticancer therapy must be discontinued at least 1 week prior to cycle 1, day 1)
  * Palliative radiotherapy for bone metastases \> 2 weeks prior to cycle 1, day 1
* Treatment with any other investigational agent within 4 weeks prior to cycle 1, day 1
* Treatment with systemic immunostimulatory agents (including, but not limited to, interferon \[IFN\]-alpha or interleukin \[IL\]-2) within 6 weeks prior to cycle 1, day 1
* Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to cycle 1, day 1

  * Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea or steroids as computed tomography \[CT\] scan contrast premedication) may be enrolled
  * The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed
* Patients taking bisphosphonate therapy for symptomatic hypercalcemia within the past 28 days; use of bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is allowed
* Patients with known primary central nervous system (CNS) malignancy or symptomatic CNS metastases are excluded, with the following exceptions:

  * Patients with asymptomatic untreated CNS disease may be enrolled, provided all of the following criteria are met:

    * Evaluable or measurable disease outside the CNS
    * No metastases to brain stem, midbrain, pons, medulla, cerebellum, or within 10 mm of the optic apparatus (optic nerves and chiasm)
    * No history of intracranial hemorrhage or spinal cord hemorrhage
    * No ongoing requirement for dexamethasone for CNS disease; patients on a stable dose of anticonvulsants are permitted
    * No neurosurgical resection or brain biopsy within 28 days prior to cycle 1, day 1
  * Patients with asymptomatic treated CNS metastases may be enrolled, provided all the criteria listed above are met as well as the following:

    * Radiographic demonstration of improvement upon the completion of CNS directed therapy and no evidence of interim progression between the completion of CNS directed therapy and the screening radiographic study
    * No stereotactic radiation or whole-brain radiation within 28 days prior to cycle 1, day 1
    * Screening CNS radiographic study \>= 4 weeks from completion of radiotherapy and \>= 2 weeks from discontinuation of corticosteroids
* Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies
* History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins
* Patients requiring treatment with a receptor activator of nuclear factor kappa-B ligand (RANKL) inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab
* Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease

  * Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HBsAg\] test and a positive anti-HBc \[antibody to hepatitis B core antigen\] antibody test) are eligible
  * Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)
* History or risk of autoimmune disease, including but not limited to systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis (02/20/2019)

  * Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone are eligible
  * Patients with controlled type 1 diabetes mellitus on a stable insulin regimen, or type 2 diabetes mellitus are eligible
  * Patients with eczema, psoriasis, lichen simplex chronicus or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions:

    * Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations
    * Rash must cover less than 10% of body surface area (BSA)
    * Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%)
    * No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids)
* History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted
* Patients with active tuberculosis (TB) are excluded
* Severe infections within 4 weeks prior to cycle 1, day 1, including but not limited to hospitalization for complications of infection, bacteremia, or severe pneumonia
* Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1
* Received oral or intravenous (IV) antibiotics within 2 weeks prior to cycle 1, day 1; patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible
* Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of need for a major surgical procedure during the course of the study
* Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study and up to 5 months after the last dose of atezolizumab (06/29/2017)

  * Influenza vaccination should be given during influenza season only (approximately October to March); patients must not receive live, attenuated influenza vaccine within 4 weeks prior to cycle 1, day 1 or at any time during the study
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial (08-JAN-2021)
* Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for a minimum of 3 years, with the exception of those with a negligible risk of metastases or death, such as carcinoma in situ of the breast or cervix
* Severe, active co-morbidity defined as follows:

  * Current (within 28 days of cycle 1, day 1) signs and/or symptoms of bowel obstruction
  * Patients who require parental hydration and/or nutrition
  * Patients who require drainage gastrostomy tube
  * Evidence of bleeding diathesis or clinically significant coagulopathy
  * Serious, non-healing or dehiscing wound, active ulcer or untreated bone fracture
  * History of hemoptysis (\>= 1/2 teaspoon of bright red blood per episode) within 1 month of study enrollment
* Significant cardiovascular or cerebrovascular disease including:

  * Uncontrolled hypertension (systolic blood pressure \[SBP\] \>= 150 and/or diastolic blood pressure \[DBP\] \>= 90)
  * History of myocardial infarction within 6 months
  * Unstable angina
  * New York Heart Association functional classification II, III or IV
  * Baseline ejection fraction =\< 50% as assessed by echocardiogram or multi-gated acquisition (MUGA)
  * Cerebral vascular accident (CVA) or transient ischemic attack (TIA) within 6 months
  * Significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or peripheral arterial thrombosis) within 6 months
* History of abdominal/pelvic or tracheoesophageal fistula or gastrointestinal perforation and/or abdominal/pelvic abscess within 6 months prior to initiation of treatment (02/20/2019)
* Pregnant or lactating patients
C: Inclusion Criteria:

* Patients enrolled after August 28, 2011 must be candidates for cytoreductive surgery and consent to have their surgical treatment determined by randomization
* Patients must have histologic diagnosis of epithelial ovarian carcinoma, peritoneal primary or fallopian tube carcinoma, which is now recurrent
* Patients with the following histologic epithelial cell types are eligible: serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, transitional cell carcinoma, malignant Brenner's tumor, or adenocarcinoma not otherwise specified (N.O.S.)
* Patients must have had a complete response to front-line platinum-taxane therapy (at least three cycles)
* A complete response to front-line chemotherapy must include: negative physical exam, negative pelvic exam and normalization of CA125, if elevated at baseline; although not required, any radiographic assessment of disease status (e.g. CT, magnetic resonance imaging \[MRI\], positron emission tomography \[PET\]/CT, etc) obtained following the completion of primary therapy should be considered negative for disease
* All patients must have also had a treatment-free interval without clinical evidence of progressive disease of at least 6 months from completion of front-line chemotherapy (both platinum and taxane); front-line therapy may have included a biologic agent (i.e. bevacizumab)
* Front-line treatment may include maintenance therapy following complete clinical or pathological response; however, maintenance cytotoxic chemotherapy must be discontinued for a minimum of 6 months prior to documentation of recurrent disease; patients receiving maintenance biological therapy or hormonal therapy are ELIGIBLE provided their recurrence is documented more than 6 months from primary cytotoxic chemotherapy completion (includes maintenance chemotherapy) AND a minimum 4 weeks has elapsed since their last infusion of biological therapy
* Patients must have clinically evident recurrent disease for the purpose of this study
* Measurable disease (Response Evaluation Criteria in Solid Tumors \[RECIST\]) is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each lesion must be more than or equal to 20 mm when measured by conventional techniques, MRI or CT, or more than or equal to 10 mm when measured by spiral CT
* Absolute neutrophil count (ANC) greater than or equal to 1,500/mm\^3, equivalent to Common Toxicity Criteria for Adverse Events version (v)4.0 (CTCAE) grade 1
* Platelets greater than or equal to 100,000/mm\^3 (CTCAE grade 0-1)
* Creatinine (non-isotope dilution mass spectrometry \[IDMS\]) =\< 1.5 x institutional upper limit normal (ULN), CTCAE grade 1
* Total bilirubin =\< 1.5 ULN (CTCAE grade 1)
* Serum glutamic oxaloacetic transaminase (SGOT)/aspartate aminotransferase (AST) =\< 2.5 times the upper limit of normal in the absence of liver metastasis; SGOT/AST \< 5.0 times ULN in the presence of liver metastasis
* Alkaline phosphatase =\< 2.5 times the upper limit of normal in the absence of liver metastasis; alkaline phosphatase \< 5.0 times ULN in the presence of liver metastasis
* This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients must have a urine protein-to-creatinine ratio (UPCR) \< 1.0 mg/dL
* This eligibility criterion does not apply to patients enrolled after August 28, 2011; patients who are not candidates for surgical cytoreduction are eligible for the chemotherapy randomization; patients are not considered candidates for surgical cytoreduction if complete cytoreduction in the estimation of the investigator is impossible or a medical infirmity precludes exploration and debulking
* Patients must have met the pre-entry requirements as specified
* Patients must have signed an approved informed consent and authorization permitting release of personal health information
* Patients must have a Gynecologic Oncology Group (GOG) performance status of 0, 1, or 2

Exclusion Criteria:

* Patients who have received more than one previous regimen of chemotherapy (maintenance is not considered a second regimen)
* Patients receiving concurrent immunotherapy, or radiotherapy
* Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis are excluded
* Patients whom have already undergone secondary cytoreduction for recurrent disease are excluded
* Patients with a prior histologic diagnosis of borderline, low malignant potential (grade 0) epithelial carcinoma that was surgically resected and who subsequently developed an unrelated, new invasive epithelial ovarian or peritoneal primary cancer are eligible provided that they meet the criteria listed above
* Patients who require parenteral hydration or nutrition and have evidence of partial bowel obstruction or perforation
* Patients who have received prior chemotherapy for any abdominal or pelvic tumor (other than ovarian, fallopian tube, and primary peritoneal) are excluded
* Patients with synchronous primary endometrial cancer, or a past history of primary endometrial cancer, are excluded, unless all of the following conditions are met: stage not greater than I-B; no more than superficial myometrial invasion, without vascular or lymphatic invasion; no poorly differentiated subtypes, including papillary serous, clear cell or other International Federation of Gynecology and Obstetrics (FIGO) grade 3 lesions
* Patients with uncontrolled infection
* Patients with concurrent severe medical problems unrelated to the malignancy that would significantly limit full compliance with the study or expose the patient to extreme risk or decreased life expectancy
* Patients with \>= grade 2 peripheral neuropathy
* Patients with a history of allergic reactions to carboplatin and/or paclitaxel or chemically similar compounds; patients with allergic (hypersensitivity) reactions to these chemotherapeutic agents are NOT excluded IF they were successfully retreated following a desensitization program or protocol
* This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibodies
* Patients of childbearing potential, not practicing adequate contraception, patients who are pregnant or patients who are nursing are not eligible for this trial; to date, no fetal studies in animal or humans have been performed; the possibility of harm to a fetus is likely; bevacizumab specifically inhibits VEGF, which is responsible for the formation of new blood vessels during development, and antibodies can cross the placenta; therefore, bevacizumab should not be administered to pregnant women; in addition, there are unknown immediate and long-term consequences of chemotherapy administration to these women; in addition, surgical exploration as mandated by randomization during pregnancy may cause imminent mortal consequences; further, it is not known whether bevacizumab is excreted in human milk; because many drugs are excreted in human milk, bevacizumab should not be administered to nursing women; subjects will be apprised of the large potential risk to a developing fetus
* Patients with other invasive malignancies, with the exception of non-melanoma skin cancer, who had (or have) any evidence of the other cancer present within the last 5 years or whose previous cancer treatment contraindicates this protocol therapy
* This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients with active bleeding or pathologic conditions that carry high risk of bleeding such as a known bleeding disorder, coagulopathy, or tumor involving major vessels
* This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients with a history or evidence upon physical examination of central nervous system (CNS) disease, including primary brain tumor, seizures not controlled with standard medical therapy, any brain metastases or a history of stroke within 5 years of the first date of treatment on this study
* This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients with clinically significant cardiovascular disease; this includes:

  * Patients with significant cardiac conduction abnormalities, i.e. PR interval \> 0.24 seconds (sec) or 2nd or 3rd degree atrioventricular (AV) block
  * Uncontrolled hypertension, defined as systolic \> 150 mm Hg or diastolic \> 90 mm Hg
  * Myocardial infarction, cardiac arrhythmia or unstable angina \< 6 months prior to registration
  * New York Heart Association (NYHA) grade II or greater congestive heart failure
  * Serious cardiac arrhythmia requiring medication
  * Grade II or greater peripheral vascular disease (exception: episodes of ischemia \< 24 hours \[hrs\] in duration, that are managed non-surgically and without permanent deficit)
  * History of cerebrovascular attack (CVA) within six months
* This criterion applies only to the patients enrolled before August 29, 2011 and those enrolled after this date electing to receive bevacizumab; patients who have had a major surgical procedure, open biopsy, dental extractions or other dental surgery/procedure that results in an open wound, or significant traumatic injury within 28 days prior to the first date of treatment on this study, or anticipation of need for major surgical procedure during the course of the study; patients with placement of vascular access device or core biopsy within 7 days prior to the first date of treatment on this study
* Patients undergoing pre-treatment secondary cytoreduction will undergo therapy with bevacizumab on cycle #2
* Patients undergoing pre-treatment surgery for purposes other than cytoreduction may also participate provided they meet eligibility; patients randomized to arms containing bevacizumab must wait a minimum of 28 days since that procedure to begin protocol treatment; patients who undergo an uncomplicated port placement must wait a minimum of 7 days to begin protocol treatment
D: Inclusion Criteria:

* Histologically proven advanced-relapsed epithelial ovarian, primary peritoneal, or fallopian tube cancer
* Eastern Cooperative Oncology Group (ECOG) performance status grade of 0 or 1
* Received first-line treatment with a platinum-based regimen and had no evidence of disease progression for \>= 6 months after the last dose
* Received second-line treatment with a platinum-based regimen, with progression of disease after attaining a response
* Progression of disease based on imaging after the second-line platinum-based regimen (individuals treated with a pegylated liposomal doxorubicin-containing regimen as a second-line therapy are eligible if subsequent disease progression occurs \>=9 months from the first dose)
* Evidence of measurable disease at screening as evaluated by Response Evaluation Criteria in Solid Tumors (RECIST) (Version 1.1)
* Participants no longer need to be able to receive intravenous (IV) dexamethasone or an equivalent IV corticosteroid
* Have a known BRCA 1/2 mutation status (for participants who do not have a known BRCA 1/2 status at screening, a blood sample will be collected to determine the status with the results available prior to randomization
* Laboratory values within protocol -defined parameters
* Have left ventricular ejection fraction by multigated acquisition scan (MUGA) scan or 2D-ECHO within normal limits for the institution
* Have side effects (except alopecia) of prior treatment resolved to at least Grade 1 according to the National Cancer Institute - Common Terminology Criteria of Adverse Events (NCICTCAE) (Version 4.0)
* Have a negative urine or serum pregnancy test at screening
* Agrees to protocol-defined use of effective contraception

Exclusion Criteria:

* Diagnosis of ovarian carcinoma with mucinous histology
* Had more than 2 prior lines of systemic therapy. Maintenance therapies and hormonal therapies are not considered additional lines of therapy
* Participants who had a prior exposure to trabectedin or hypersensitivity to any of the excipients will not be excluded from receiving single-agent Doxil
* Prior treatment with doxorubicin or other anthracycline at cumulative doses greater than 300 mg/m2 (calculated using doxorubicin equivalent doses: 1 mg doxorubicin = 1 mg Doxil/Caelyx = 1.8 mg epirubicin = 0.3 mg mitoxantrone = 0.25 mg idarubicin)
* Participants unwilling or unable to have a central venous catheter placed will not be excluded from receiving single-agent Doxil
* Pregnant or breast-feeding
* Would receive study treatment within 3 weeks from radiation therapy, experimental therapy, hormonal therapy, prior chemotherapy, or biological therapy; use an invasive investigational device; or is currently enrolled in an investigational study
* History of another invasive malignancy (except non-metastatic basal cell carcinoma or squamous cell carcinoma of the skin or cervical carcinoma in situ adequately treated) unless in remission for \>=5 years, or a non - invasive malignancy requiring ongoing therapy
* Known allergies, hypersensitivity, or intolerance to Doxil, dexamethasone, or their excipients
* Known history of central nervous system metastasis
* Known significant chronic liver disease, such as cirrhosis or active hepatitis (potential participants who test positive for hepatitis B surface antigen or hepatitis C antibodies are allowed provided they do not have active disease requiring antiviral therapy)
* Had a myocardial infarct within 6 months before enrollment, New York Heart Association (NYHA) Class II or greater heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, clinically significant pericardial disease, or electrocardiographic evidence of acute ischemic or active conduction system abnormalities
* Has any of the following medical conditions: uncontrolled diabetes, psychiatric disorder (including dementia) that prevents compliance with protocol, uncontrolled seizures, newly diagnosed deep vein thrombosis, active systemic infection that is likely to interfere with study procedure or results
* Has any condition that, in the opinion of the investigator, would compromise the well-being of the participant or the study or prevent the participant from meeting or performing study requirements

Answer: C