Talazoparib in Treating Patients With Recurrent, Refractory, Advanced, or Metastatic Cancers and Alterations in the BRCA Genes

Inclusion Criteria: * Patients with advanced or metastatic cancer that is refractory to standard therapy or has relapsed after standard therapy * Patients must have one of the following: somatic mutations or deletions in BRCA1 or BRCA2; genomic alterations in other BRCA pathway genes (subcohorts: a. ATM, b. PALB2, c. other genes, e.g. Fanconi Anemia genes, ARID1A, MER11, RAD50, NBS1, ATR; amplification of EMSY); or germline mutation in BRCA1 or BRCA 2 (not breast or ovarian cancer) * Patients must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-1 * Absolute neutrophil count \>= 1500/mL * Platelets \>= 100,000/mL * Hemoglobin \>= 9 g/dL (or \>= 5.6 mmol/L) * Serum creatinine =\< 1.5 x upper limit of normal (ULN) (or glomerular filtration rate \[GFR\] \>= 60 ml/min for patients with creatinine \> 1.5 x ULN) * Serum total bilirubin =\< 1.5 x ULN (direct bilirubin =\< ULN if total bilirubin \[bili\] \> 1.5 x ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN (or =\< 5 x ULN if liver metastases \[mets\]) * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants; activated PTT (aPTT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Patients must be \>= 4 weeks beyond treatment with any chemotherapy or other investigational therapy to include hormonal, biological, or targeted agents; or at least 5 half-lives from hormonal, biological, or targeted agents, whichever is shorter at the time of treatment initiation * Women of child-bearing potential MUST have a negative serum or urine human chorionic gonadotropin (HCG) test unless prior tubal ligation (\>= 1 year before screening), total hysterectomy or menopause (defined as 12 consecutive months of amenorrhea); patients should not become pregnant or breastfeed while on this study; sexually active patients must agree to use dual contraception for the duration of study participation and for 120 days after the last dose of talazoparib * Ability to understand and willingness to sign informed consent form prior to initiation of the study and any study procedures * Patients need to have biopsiable disease to enroll on cohort 1-2; patients eligible for cohort 3 with a germline BRCA alteration can be enrolled even if they do not have biopsiable disease Exclusion Criteria: * Patients who are pregnant or breastfeeding * Prior treatment with a PARP inhibitor * Known hepatitis B, hepatitis C or human immunodeficiency virus (HIV) infection * Inability or unwillingness to swallow pills * Active infection requiring intravenous (IV) antibiotics or other uncontrolled intercurrent illness requiring hospitalization * Any medical condition or diagnosis that would likely impair absorption of an orally administered drug (e.g. gastrectomy, ileal bypass, chronic diarrhea, gastroparesis) * Inability to comply with the study and follow-up procedures * History of cerebrovascular accident (CVA), myocardial infarction or unstable angina within the previous 6 months before starting therapy * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has a known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis which is excluded regardless or clinical stability