Avelumab and Trabectedin in Treating Patients With Liposarcoma or Leiomyosarcoma That is Metastatic or Cannot Be Removed by Surgery

This phase I/II studies the side effects of avelumab and trabectedin and how well they work in treating patients with leiomyosarcoma or liposarcoma that has spread to other places in the body (metastatic) or cannot be removed by surgery. Immunotherapy with monoclonal antibodies, such as avelumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Drugs used in chemotherapy, such as trabectedin, 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. Giving avelumab and trabectedin may work better in treating patients with liposarcoma or leiomyosarcoma.

PRIMARY OBJECTIVES:

I. To assess the safety and tolerability of the combination of trabectedin and avelumab in subjects with advanced leiomyosarcoma and liposarcoma.

II. To assess the objective response rate of advanced L-type sarcoma patients receiving the combination regimen of avelumab and trabectedin.

SECONDARY OBJECTIVE:

I. To further explore the clinical activity and safety profile of avelumab and trabectedin as a combination therapy.

OUTLINE:

Avelumab will be administered every 2 weeks. Trabectedin will be administered every 3 weeks for the first two doses (Week 1 and Week 4), and then every four weeks (Week 7, Week 11,...) moving forward. After Cycle 2 of trabectedin, dosing may extend to every 5 weeks at investigator discretion, for management of trabectedin-associated toxicity only. Delays of trabectedin beyond 5 weeks may be allowed but require written approval from the Sponsor-Investigator. On days where both drugs are scheduled to be administered, avelumab will be administered first. This will continue until unacceptable toxicity or confirmed disease progression.

After completion of study treatment, patients are followed up at 30 and 90 days, then every 12 weeks for 2 years.

Eligibility Criteria:
Inclusion Criteria:

* Must have a histologically confirmed diagnosis of advanced (metastatic or unresectable) soft tissue sarcoma with one of the following subtypes:

  * Leiomyosarcoma
  * Liposarcoma
* Subject must be clinically indicated to receive trabectedin therapy as part of routine care. Subjects may be first line, or have received any number of prior systemic therapies
* Total bilirubin level =\< 1.5 x the upper limit of normal (ULN) mg/dL
* Aspartate aminotransferase (AST) =\< 2.5 x ULN and alanine aminotransferase (ALT) =\< 2.5 x ULN
* Alkaline phosphatase \< 2.5 x ULN
* Serum creatinine =\< 1.5 x ULN
* Calculated creatinine clearance \>= 30 mL/min using the Cockcroft-Gault formula may be included
* Creatinine phosphokinase (CPK) =\< 2.5 x ULN
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L
* Platelet count \>= 100,000/mm\^3 (100 x 10\^9/L)
* Hemoglobin \>= 9 g/dL
* Subject must demonstrate a left ventricular ejection fraction (LVEF) \> 45% by echocardiography (ECHO) or multigated acquisition scan (MUGA)
* Male or non-pregnant and non-breast feeding female:

  * Females of child-bearing potential must agree to use highly effective contraception without interruption from initiation of therapy and while on study medication and have a negative serum pregnancy test (beta - human chorionic gonadotropin \[hCG\]) result at screening and agree to ongoing pregnancy testing during the course of the study, and at the end of study treatment; a highly effective method of contraception is defined as one that results in a low failure rate (that is, \< 1% per year), when used consistently and correctly, such as implants, injectables, combined oral contraceptives, some intrauterine contraceptive devices, sexual abstinence, or a vasectomized partner
  * Male subjects must practice abstinence or agree to use a condom during sexual contact with a pregnant female or a female of childbearing potential while participating in the study
* All ongoing toxicities related to prior therapies must be resolved to grade 1 or better (except alopecia)
* Subject must have an Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 or Karnofsky performance scale \>= 70
* Subjects must have one or more measurable lesions, as determined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 assessed by computed tomography (CT) or magnetic resonance imaging (MRI)
* Subjects must have a life expectancy of \>= 6 months, as determined by the treating physician
* Ability to understand and sign informed consent document
* Willingness and ability to comply with the scheduled visits, laboratory tests, and other study procedures

Exclusion Criteria:

* Known active, uncontrolled, or symptomatic central nervous system (CNS) metastases; a subject with controlled and asymptomatic CNS metastases may participate in this study; as such, the subject must have completed any prior treatment for CNS metastases \>= 28 days (including radiotherapy and/or surgery) prior to the start of treatment in this study and should not be receiving chronic corticosteroid therapy in excess of 10 mg daily prednisone (or equivalent) for CNS metastases; subjects with known CNS metastases must be confirmed radiographically stable by at least one imaging study, at least 28 days from last treatment
* Receipt of any type of cytotoxic, biologic, or other systemic anticancer therapy (including investigational) within 2 weeks of enrollment
* Prior organ transplantation, including allogeneic stem cell transplantation
* Prior treatment with trabectedin
* Significant acute or chronic infections including, among others:

  * Known history of testing positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS)
  * Known active infection with hepatitis B or hepatitis C
* Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent:

  * Subjects with diabetes type I, vitiligo, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible
  * Subjects requiring hormone replacement with corticosteroids are eligible if the steroids are administered only for the purpose of hormonal replacement and at doses =\< 10 mg or 10 mg equivalent prednisone per day
  * Administration of steroids through a route known to result in a minimal systemic exposure (topical, intranasal, introocular, or inhalation) are acceptable
* Known severe hypersensitivity reactions to monoclonal antibodies (grade \>= 3 National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\] 5.0), any history of anaphylaxis, or uncontrolled asthma (that is, 3 or more features of partially controlled asthma)
* Pregnant or lactating females
* Known, active alcohol or drug abuse
* All other significant diseases (for example, inflammatory bowel disease, uncontrolled asthma), which, in the opinion of the investigator, might impair the subject's tolerance of trial treatment
* Any vaccination within 4 weeks of the first dose of avelumab, with the following exceptions:

  \* Administration of inactivated vaccines, including inactivated flu vaccines, are allowable; however, they should not be given within 2 weeks prior to starting study treatment
* Clinically significant cardiovascular disease including cerebral vascular accident/stroke (\< 6 months prior to enrollment), myocardial infarction (\< 6 months prior to enrollment), congestive heart failure with New York Heart Association (NYHA) class II or greater or serious cardiac arrhythmia requiring medication
* Severe (requiring active treatment) acute or chronic medical conditions including: colitis, inflammatory bowel disease, pneumonitis, or pulmonary fibrosis
* Recent (within the past year) or active suicidal ideation or behavior