Talazoparib and Avelumab in Participants With Metastatic Renal Cell Carcinoma

Inclusion Criteria: * Biopsy proven, histological confirmed renal cell carcinoma (RCC) or renal medullary carcinoma (RMC).. Patients with surgery and biopsy at outside institutions will be eligible for this protocol once archival material is reviewed and the above diagnosis confirmed by genitourinary pathology review at Memorial Sloan Kettering Cancer Center (MSKCC). Cohort 1: (Closed to Accrual) * Presence of VHLalteration by next-generation sequencing (NGS) with a stateapproved assay * Patients must have radiographic evidence of disease progression after treatment with at least one prior PD-1 or PD-L1 agent, and one prior VEGF inhibitor * Maximum 3 prior lines of therapy Cohort 2: * For FH/SDH patients FH- or SDH- expression-loss by immunohistochemistry (IHC) or alteration (somatic or germline) in FH or SDH per NGS with a state-approved assay * For Renal Medullary Carcinoma (RMC) patients: histologic confirmation of RMC (no IHC/NGS criteria required) * At least one prior line of therapy: * For FH/SDH patients Patients must have radiographic evidence of disease progression after treatment with at least one prior line of therapy (one prior PD-1/PD-L1 and/or VEGF inhibitor). * For Renal Medullary Carcinoma (RMC) patients prior radiographic evidence of disease progression on/after at least one line of chemotherapy (e.g. carboplatin / paclitaxel, carboplatin / paclitaxel / bevacizumab, carboplatin / gemcitabine, and gemcitabine / doxorubicin). * No maximum lines of therapy Both Cohorts 1 \& 2 * Adequate Hematologic Function * Absolute Neutrophil Count ≥ 1.5 x 10\^9 / L * Platelet Count ≥ 100 x 10\^9 / L * Hemoglobin ≥ 9 g/dL * No transfusion of packed red blood cells or platelets within 21 days of Cycle 1 Day 1 * Adequate Renal Function ≥ 30 ml/min according to the Cockcroft-Gault Equation * Patients with moderate renal impairment (creatinine clearance 30-59 by Cockcroft-Gault EquationI) will start with a reduced dose of talazoparib. * Adequate Hepatic Function including: * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) * AST ≤ 3 x upper limit of normal (ULN) without liver metastasis * ALT ≤ 3 x upper limit of normal (ULN) without liver metastasis * AST or ALT ≤ 5 x upper limit of normal (ULN) for patients with liver metastasis * Patients with known Gilbert's syndrome may be included if total bilirubin ≤ x 3 ULN * Eastern Cooperative Group (ECOG) Performance Status 0-2. * Patients must have measurable disease by RECIST v1.1. At least one measurable lesion should not have been previously irradiated. * Women of childbearing potential must have negative serum pregnancy testing at screening. All women will be considered childbearing potential unless meeting criteria including: * Achieved post-menopausal status as defined by cessation of regular menses for at least 12 consecutive months with no alternative pathological or physiological cause and have follicular stimulation hormone showing postmenopausal state. Women who have been amenorrhoeic for ≥12 months are still considered to be of childbearing potential if the amenorrhea is possibly due to prior chemotherapy, anorexia, low body weight, ovarian suppression, anti-estrogen therapy or other medically inducible reasons. * Documented hysterectomy or bilateral oophorectomy surgery * Medically confirmed ovarian failure * Sexually active participants and their partners must agree to use medically accepted methods of contraception (i.e. barrier methods including condoms, female condom, or diaphragm with spermicidal gel) during the study and for 7 months after the last dose of the study treatment for females, and 4 months for males. * Recovery of baseline CTCAE v5.0 grade ≤1 toxicities related to prior study treatments unless adverse events are clinically non-significant and/or stable on supportive therapy if needed. * Patients must be willing and able to comply with trial protocol. This includes adhering to the treatment plan, scheduled visits, laboratory and other study procedures. Exclusion Criteria: * Patients \< 18 years old * Patients who are pregnant or breast-feeding. Fertile patients who are unwilling or unable to use two methods of contraception (at least one of which considered highly effective) for duration of study and after 7 months after last dose of study treatment for female, and 4 months for males. * Patients who had prior immune checkpoint blockade therapy (either anti-PD-1, anti- PD-L1 and/or anti-CTLA-4) discontinued due to development of an immune related adverse event. * Prior diagnosis of myelodysplastic syndrome (MDS) or diagnosis of other malignancy that requires anti-cancer directed therapy within the last 24 months. Exclusions include those cancers that are considered cured by local therapy (i.e.Basal cell carcinoma, squamous cell carcinoma, ducal carcinoma in situ of breast, bladder of cervix) or other cancers that have low malignant potential and do not require systemic therapy (i.e. Gleason-grade \<6 prostate adenocarcinoma, borderline ovarian malignancy / low malignant potential). * Prior treatment with talazoparib or other agents that target PARP * Treatment with anti-cancer therapies within 21 days or five half-lives, whichever shorter, of start date, including monoclonal antibody, cytotoxic therapy, or another investigational agent. There is no specific time window between last PD-1/PD-L1 therapy and start date of new therapy on protocol. * Significant vascular disease (i.e. aortic aneurysm requiring surgical repair, recent arterial thrombosis) within 6 months prior to first dose of therapy. * Evidence of bleeding diathesis or significant unexplained coagulopathy (i.e. absent of anticoagulation) * Clinical signs or symptoms of gastrointestinal obstruction requirement parenteral hydration, parenteral nutrition, or feeding tube. * Uncontrolled effusion management (pleural effusion, pericardial effusion, or ascites) which requires recurrent drainage procedures. * Patients treated with systemic immunosuppressants; except for 1. chronic physiologic replacement of ≤ 10mg prednisone (or equivalent) for treatment of adrenal insufficiency; Steroids required for pre-medication reactions 2. Local steroid use is permitted (e.g. intranasal, topical, inhaled, or local steroid injection, i.e. intra-articular) * Patients with autoimmune disease that may worsen during immune checkpoint blockade therapy are excluded. Patients with diabetes type I, vitiligo, psoriasis, hypo- or hyperthyroid disease not requirement immunosuppressive treatment as above are eligible. * Prior organ transplantation including allogeneic stem cell transplant. * No active infection requiring parenteral antibiotic therapy. * Prior diagnosis of HIV/AIDS * History of either positive HCV RNA viral load or anti-HCV antibody screening detectable; HBV infection with HBV surface antigen detection and/or positive HBV DNA viral load. * Known hypersensitivity to talazoparib or avelumab, or any component in formulations. Patients with known hypersensitivity to monoclonal antibodies (Grade ≥3 by CTCAE v5.0) * Live vaccination within 4 weeks of first dose of therapy. All vaccines except inactivated are prohibited while on study. * Severe acute or chronic medical conditions which may significantly increase the risk of study participants, per treating investigator's discretion * Radiation therapy to any site (including bone) \<2 weeks prior to the first dose of therapy. Patients with clinically relevant ongoing complications from prior radiation therapy, per investigators' assessment, are not eligible. * Symptomatic brain metastasis or leptomeningeal disease requiring steroid use. Patients are eligible if they neurologically stable for 4 weeks, and have completed radiation therapy or surgery, and recovered from side effects. Patients must have discontinued steroid therapy for at least 2 weeks prior to first dose of study treatment. * Current or anticipated use of potent P-gp inhibitors within 7 days prior to randomization or anticipated use during the study. Please see Appendix 5 for a list of potent P-gp inhibitors. * Inability to swallow capsules, known intolerance to talazoparib or its excipients, known malabsorption syndrome, or other conditions which impair intestinal absorption. * Investigator site staff members directly involved in study conduct, including but not limited to their family members, or patients who are Pfizer members, including their family members, who are directly involved in study conduct.