Talazoparib and Radiation Therapy in Treating Patients With Locally Recurrent Gynecologic Cancers

Inclusion Criteria: * Provision of informed consent prior to any study specific procedures * Histologically-confirmed recurrent ovarian, fallopian tube, primary peritoneal cancer, endometrial, vaginal, or cervical cancer in the abdomen and pelvis * Subjects with stage IV disease are eligible as long as disease elsewhere (other than the site(s) to receive radiation therapy \[RT\]) is undetectable or stable (\>= 3 months) and immediate chemotherapy is not required. Willingness to discontinue any cytotoxic chemotherapeutic agents, immunotherapy, biologic therapy, and targeted therapies at least three weeks prior to start of investigational therapy * Hemoglobin \>= 10.0 g/dL and no blood transfusions in the 28 days prior to entry/randomization (choose whichever is most applicable to the study) (within 28 days prior to administration of study treatment) * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (within 28 days prior to administration of study treatment) * No features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) on peripheral blood smear (within 28 days prior to administration of study treatment) * White blood cells (WBC) \> 3 x 10\^9/L (within 28 days prior to administration of study treatment) * Platelet count \>= 100 x 10\^9/L (within 28 days prior to administration of study treatment) * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (within 28 days prior to administration of study treatment) * Aspartate aminotransfera…