Brief Summary: This phase I trial studies the side effects and best dose of talazoparib in combination with radiation therapy and to see how well they work in treating patients with gynecologic cancers that have come back after previous treatment (recurrent). Talazoparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Giving talazoparib in combination with radiation therapy may work better in treating patients with gynecologic cancers.

Detailed Description: PRIMARY OBJECTIVE: I. To determine the safety, tolerability, and maximally tolerated dose (MTD) of talazoparib combining talazoparib and fractionated radiotherapy in patients with refractory or recurrent ovarian, fallopian tube, primary peritoneal, cervical, or vaginal or endometrial carcinoma. SECONDARY OBJECTIVES: I. To determine the safety profile of talazoparib in combination with fractionated radiotherapy for recurrent gynecologic cancers. II. To determine a preliminary anti-cancer activity of this combination at the MTD. EXPLORATORY OBJECTIVES: I. To explore the potential feasibility of using biomarkers in tumor tissue, whole blood or serum as predictive markers of treatment response. II. To explore the impact of talazoparib when combined with radiotherapy for recurrent gynecologic cancers on 1) patient reported acute gastrointestinal (GI) toxicity and 2) overall longitudinal quality of life at week 5 of therapy. OUTLINE: This is a dose escalation study of talazoparib. Patients receive talazoparib orally (PO) once daily (QD) beginning on days -10 to -7 and continuing for up to 8 weeks in the absence of disease progression or unacceptable toxicity. Patients also undergo radiation therapy 5 days a week (Monday-Friday) for up to 7 weeks. After completion of study treatment, patients are followed up at 1, 3, 6, 9, and 12 months, and then every 6 months for up to 1 year.