Nivolumab in Combination With Talazoparib in Melanoma and Mutations in BRCA or BRCA-ness Genes

Inclusion Criteria: * Subjects must have a germline or somatic DNA damage repair mutation including any one of the following: BRCA1, BRCA2, ATM, CHEK1, CHEK2, PALB2, RAD50, RAD51, NBN, BLM, BRIP1, ATR, PARP1, MDC1, DSS1, ERCC3, MRE11, HDAC2, FANCA, MLH3, MLH1, EMSY, BAP1, LIG4, LIG3, PRKDC, XRCC6. The result may have been obtained from one of the following test providers: Myriad Genetics, Invitae, Ambry, Quest, Color Genomics, IMPACT, Foundation Medicine (tissue or ctDNA based), Guardant, or another CLIA approved tissue and/or serum based next generation sequencing-based assay. * Subjects must have histologically or cytologically confirmed diagnosis of primary or recurrent metastatic melanoma. * Subjects must have received prior checkpoint inhibitor therapy (defined as anti-CTLA4 or anti-PD-1 or combination anti-CTLA4/anti-PD-1), either for metastatic or unresectable disease or adjuvant therapy. * ECOG Performance status ≤ 2. * Subjects must have normal organ and marrow function as defined below: * Hemoglobin ≥ 9.0 g/dl * Absolute neutrophil count ≥ 1,500/mcL * Platelet count ≥ 90,000/mcL * Bilirubin ≤ 1.5 x ULN (except in subjects with Gilbert Syndrome, who can have a total bilirubin \< 3.0mg/dL) * AST (SGOT) ≤ 3.0 X upper limit of normal * ALT (SGPT) ≤ 3.0 X upper limit of normal * Serum Creatinine Clearance ≥ 30mL/minute. See section 7.1 for talazoparib dose adjustment for renal impairment. * CrCl\< 30mL/minute has not been studied in talazoparib. * Measurable disease as defined by RECIST 1.1 criteria * During screening, while taking study drug, and until 5 months after taking the final dose of study drug, women of childbearing potential (WOCBP) must practice one of the following methods of birth control: * Use double-barrier contraception method defined as male use of a condom and female use of a barrier method (e.g., contraceptive sponge, spermicidal jelly or cream, diaphragm \[always use with spermicidal jelly/cream\]). * Use of hormonal contraceptives (oral, parenteral, vaginal, or transdermal) for at least 3 months before the first study drug administration. * Use of an intrauterine device. * Have a male partner who has had a vasectomy (at least 6 months prior to study enrollment). * Or must abstain from sexual intercourse completely. * During screening, while taking study drug, and until 7 months after taking the final dose of study drug, men who are sexually active with WOCBP must practice one of the following methods of birth control: * Have had a vasectomy (at least 6 months prior to study enrollment). * Use double-barrier contraception method defined as male use of a condom and female use of a barrier method (e.g., contraceptive sponge, spermicidal jelly or cream, diaphragm \[always use with spermicidal jelly/cream\]). * Partner use of an intrauterine device. * Partner use of hormonal contraceptives (oral, parenteral, vaginal, or transdermal) for at least 3 months before the first study drug administration. * Or must abstain from sexual intercourse completely * Subjects must have the ability to understand and the willingness to sign a written informed consent document. * Ability to swallow pills. Exclusion Criteria: * Prior treatment with a PARP inhibitor. * Prior anti-cancer therapy for melanoma less than 14 days prior to first dose of study drug. * Known symptomatic brain metastases requiring steroids. Patients with previously diagnosed brain metastases are eligible if they have completed their treatment and have recovered from the acute effects of radiation therapy or surgery prior to study enrollment, have discontinued corticosteroid treatment for these metastases for at least 4 weeks and are neurologically stable. * Subjects with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Known HIV or AIDS-related illness HIV-positive subjects on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with talazoparib. In addition, these subjects are at increased risk of lethal infections when treated with marrow suppressive therapy. Appropriate studies will be undertaken in subjects receiving combination antiretroviral therapy when indicated. * Prior organ transplantation including allogeneic stem-cell transplantation. * Poorly controlled or uncontrolled autoimmune disease that might deteriorate when receiving an immunostimulatory agent. Subjects with vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition or prior therapy requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. Patients with endocrinopathies controlled on replacement drugs are eligible. * Major surgery within 4 weeks prior to study enrollment. * Current use of corticosteroids at the time of study enrollment, EXCEPT for the following: * a. Intranasal, inhaled, topical steroids, eye drops or local steroid injection (eg, intra-articular injection) * b. Systemic corticosteroids at physiologic doses ≤10 mg/day of prednisone or equivalent * c. Steroids as premedication for hypersensitivity reactions (eg, CT scan premedication) * Diagnosis of Myelodysplastic Syndrome (MDS) * Active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening (positive HBV surface antigen or detectable HCV RNA if anti-HCV antibody screening test positive). * Current or anticipated use of a P-glycoprotein (P-gp) inhibitor (amiodarone, carvedilol, clarithromycin, cobicistat, darunavir, dronedarone, erythromycin, indinavir, itraconazole, ketoconazole, lapatinib, lopinavir, propafenone, quinidine, ranolazine, ritonavir, saquinavir, telaprevir, tipranavir, valspodar, and verapamil), P-gp inducer (avasimibe, carbamazepine, phenytoin, rifampin, and St. John's wort), or inhibitor of breast cancer resistance protein (BCRP) (curcumin, cyclosporine, elacridar \[GF120918\], and eltrombopag). * Inability to swallow capsules or known intolerance to talazoparib or its excipients. * Pregnant women are excluded from this study because animal studies have demonstrated that nivolumab and talazoparib may cause fetal harm when administered to pregnant women. Breastfeeding women are excluded from this study because nivolumab and talazoparib may be excreted in human breastmilk and the potential for serious adverse reactions in nursing infants. * Persisting toxicity related to prior therapy \> Grade 1.