Inclusion Criteria:  Participant must have histologically documented LMS. Pathology review and confirmation of diagnosis will occur at the site enrolling the patient on this study.  Patients must have had a recent, within six months of screening, tumor biopsy testing positive for pathogenic mutation or homozygous loss of either BARD1, BRCA1, BRCA2, BRIP1, PALB2, RAD51, RAD51B, RAD51C, or RAD51D using a clinically validated next-generation (NGS) sequencing panel.  Variant pathogenicity will be arbitrated by the primary investigative team Patients must have locally advanced and unresectable or metastatic disease Patients must have disease which is measurable at study entry according to Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. Additionally, patients must have a site of disease deemed accessible for biopsy at no or minimal risk to the patient (including through the use of image-guidance). If there are questions regarding the feasibility of biopsy, the case should be reviewed with interventional radiology or the appropriate department at the study site Patients must have had prior progression on, or intolerance to, at least one line of systemic therapy for advanced LMS. Adjuvant therapy administered after curative resection will not qualify as prior treatment. There is no upper limit on the number of prior therapies received Participant must have an Eastern Cooperative Oncology Group (ECOG) performance status of =< 2 Participant must be >= 18 years of age Absolute neutrophil count >= 1,500/uL Platelets >= 100,000/uL Hemoglobin >= 9 g/dL Serum creatinine =< 1.5 x upper limit of normal (ULN) or calculated creatinine clearance >= 30 mL/min using the Cockcroft-Gault equation Total bilirubin =< 1.5 x ULN (=< 2.0 in patients with known Gilbert's syndrome) OR direct bilirubin =< 1 x ULN Aspartate aminotransferase and alanine aminotransferase =< 2.5 x ULN unless liver metastases are present, in which case they must be =< 5 x ULN Participant receiving corticosteroids may continue as long as their dose is stable for least 4 weeks prior to initiating protocol therapy  Female participant has either a negative highly sensitive urine or a serum pregnancy test within 72 hours prior to taking study treatment if of childbearing potential and agrees to abstain from activities that could result in pregnancy from screening through 180 days after the last dose of study treatment, or is of nonchildbearing potential. Nonchildbearing potential is defined as follows (by other than medical reasons):  >= 45 years of age and has not had menses for > 1 year Patients who have been amenorrhoeic for < 2 years without history of a hysterectomy and oophorectomy must have a follicle stimulating hormone value in the postmenopausal range upon screening evaluation Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure, otherwise the patient must be willing to use 2 adequate barrier methods throughout the study, starting with the screening visit through 180 days after the last dose of study treatment. Information must be captured appropriately within the site's source documents. Note: Abstinence is acceptable if this is the established and preferred contraception for the patient. Females on hormone replacement therapy (HRT) and whose menopausal status is in doubt will be required to use one of the non-estrogen hormonal highly effective contraception methods if they wish to continue their HRT during the study. Otherwise, they must discontinue HRT to allow confirmation of postmenopausal status before study enrollment Male participant agrees to use an adequate method of contraception starting with the first dose of study treatment through 90 days after the last dose of study treatment. Note: Abstinence is acceptable if this is the established and preferred contraception for the patient Participant must be able to understand the study procedures and agree to participate in the study by providing written informed consent Participant must have normal blood pressure or adequately treated and controlled hypertension (i.e. systolic blood pressure =< 140 mmHg and diastolic blood pressure =< 90 mmHg).  Exclusion Criteria:  Patients must not have had any previous treatment with any poly(adenosine diphosphate[ADP]-ribose) polymerase (PARP) inhibitors Participant must not be simultaneously enrolled in any interventional clinical trial Participant must not have had major surgery =< 4 weeks prior to initiating protocol therapy and participant must have recovered from any surgical effects Participant must not have received investigational therapy =< 4 weeks, or within a time interval less than at least 5 half-lives of the investigational agent, whichever is shorter, prior initiating protocol therapy Participant receiving non-steroidal anti-estrogen agents must discontinue their use at least two weeks prior to study entry Participant has had radiation therapy encompassing > 20% of the bone marrow within 2 weeks; or any radiation therapy within 1 week prior to Day 1 of protocol therapy Participant must not have a known hypersensitivity to niraparib components or excipients. Participant must not have received a transfusion (platelets or red blood cells) =<4 weeks prior to initiating protocol therapy Participant must not have received colony-stimulating factors (e.g., granulocyte colony-stimulating factor, granulocyte macrophage colony-stimulating factor, or recombinant erythropoietin) within 4 weeks prior to initiating protocol therapy Participant has had any known Grade 3 or 4 anemia, neutropenia or thrombocytopenia due to prior chemotherapy that persisted > 4 weeks and was related to the most recent treatment Participant must not have any known history or current diagnosis of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML) Participant must not have a serious, uncontrolled medical disorder, nonmalignant systemic disease, or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 90 days) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, or any psychiatric disorder that prohibits obtaining informed consent Participant must not have had diagnosis, detection, or treatment of another type of cancer =< 2 years prior to initiating protocol therapy (except basal or squamous cell carcinoma of the skin and cervical cancer that has been definitively treated)  Participant has leptomeningeal disease, carcinomatous meningitis, symptomatic brain metastases, or radiologic signs of central nervous system (CNS) hemorrhage.  Note: Participants with asymptomatic brain metastases (i.e. off corticosteroids and anticonvulsants for at least 7 days) are permitted Participant has known active hepatitis B (e.g., hepatitis B surface antigen [HBsAg] reactive) or hepatitis C (e.g., hepatitis C virus [HCV] ribonucleic acid [qualitative] is detected). Prior history of posterior reversible encephalopathy syndrome (PRES) History of severe renal impairment History of severe liver impairment Any clinically significant gastrointestinal (GI) abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach and/or bowels.