Measuring the Effects of Talazoparib in Patients With Advanced Cancer and DNA Repair Variations

Inclusion Criteria:

* Adult patients with solid tumors and documented germline or somatic aberrations in genes involved in DNA damage response (DDR) and whose disease has progressed following at least one standard therapy or who have no acceptable standard treatment options. Molecular testing performed at an National Cancer Institute-Molecular Analysis for Therapy Choice (NCI-MATCH) (NCT02465060) study-designated Clinical Laboratory Improvement Act (CLIA) laboratory or at Myriad Genetics, GeneDx, Invitae, or the Frederick National Laboratory for Cancer Research (FNLCR) Molecular Characterization Laboratory (MoCha) will be acceptable for determination of eligibility
* Patients with the following germline or somatic genetic aberrations will be eligible based on compelling preclinical and/or clinical data suggesting that these deleterious mutations confer sensitivity to PARP inhibitors; no more than 6 patients (across both cohorts) with an eligibility mutation in any one gene will be enrolled

  * Deleterious BRCA1 or BRCA2 mutations
  * Loss of function mutations (including novel loss of function frameshift or nonsense mutations) in the following Fanconi anemia genes: FANCA, FANCB, FANCC, FANCD2, FANCE, FANCF, FANCG, FANCI, FANCJ, FANCL, FANCM, FANCN
  * A known functional mutation (including novel loss of function frameshift or nonsense mutations) in any of the following DDR genes: ARID1A, ATM, ATR, BACH1 (BRIP1), BAP1, BARD1, CDK12, CHK1, CHK2, IDH1, IDH2, MRE11A, NBN, PALB2, RAD50, RAD51, RAD51B, RAD51C, RAD51D, RAD54L
* Age \>= 18 years of age
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Life expectancy of greater than 3 months
* Leukocytes \>= 3,000/mcL
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Hemoglobin \>= 10 g/dL
* Total bilirubin =\< 1.5 x institutional upper limit of normal (=\< 3 x upper limit of normal in the presence of documented Gilbert's syndrome or liver metastases at baseline)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) / alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal
* Creatinine =\< 1.5 x institutional upper limit of normal OR Creatinine clearance (CrCl) \>= 60 mL/min/1.73m\^2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73m\^2
* Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with CT scan, MRI, or calipers by clinical exam
* Patients must have a tumor site amenable to biopsy. If avoidable, the lesion for biopsy should not be selected as a target lesion for RECIST measurements
* The effects of talazoparib on the developing human fetus are unknown. For this reason and because PARP inhibitors are known to be teratogenic, women of child-bearing potential must agree to use a highly effective method of contraception for the duration of study participation and for at least 7 months after completing study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Male patients with female partners of reproductive potential and pregnant partners who are treated or enrolled on this protocol must also agree to use adequate contraception for the duration of study participation and for at least 4 months after completion of talazoparib administration
* Patients must be able to swallow whole tablets or capsules. Nasogastric or gastric-tube (G-tube) administration is not allowed. Any gastrointestinal disease which would impair ability to swallow, retain, or absorb drug is not allowed
* Ability to understand and the willingness to sign a written informed consent document
* Patients must have recurrent, locally advanced or metastatic disease
* Patients must have progressed on or after at least one line of standard-of-care (SOC) intervention, except for those patients without SOC or for whom talazoparib is SOC
* PATIENTS WITH OVARIAN CANCER:
* All patients with ovarian cancer should have one prior platinum-based therapy
* Patients with ovarian cancer with platinum-sensitive disease are eligible. Patients with platinum-refractory disease are not eligible
* Patients with gBRCAm ovarian cancer must also have progressed on a PARP inhibitor. The time and treatment between the prior PARP inhibitor and protocol initiation must be documented
* PATIENTS WITH PANCREATIC CANCER:
* All patients with pancreatic cancer should have received prior platinum-containing therapy in the metastatic setting
* PATIENTS WITH BREAST CANCER:
* Patients with HER2+ breast cancer should have had 2 prior systemic lines of therapy in the metastatic setting, including anti-HER2 therapy
* Patients with breast cancer who are eligible for a PARP inhibitor by Food and Drug Association (FDA) approvals must have had prior PARP inhibitor as per FDA indication. The time and treatment between the prior PARP inhibitor and protocol initiation must be documented
* PATIENTS WITH GASTRIC CANCER:
* Patients with HER2+ gastric cancer should have had received anti-HER2 therapy in the metastatic setting
* PATIENTS WITH PROSTATE CANCER:
* Patients with prostate cancer who are eligible for a PARP inhibitor by FDA approvals must have had prior PARP inhibitor for eligibility. The time and treatment between the prior PARP inhibitor and protocol initiation must be documented
* All patients with prostate cancer can continue to receive treatment with gonadotropin-releasing hormone (GnRH) agonists while on study, as long as there is evidence of disease progression on prior therapy
* Patients with castration resistant prostate cancer must have castrate levels of testosterone (\< 50 ng/dL \[1.74 nmol/L\])
* Patients with metastatic hormone receptor (HR) prostate cancer and mutations in either BRCA1, BRCA2, or ATM should continue to receive anti-androgen receptor (anti-AR) therapy

Exclusion Criteria:

* Patients who have had chemotherapy or radiotherapy within 4 weeks or 5 half-lives, whichever is shorter (6 weeks for nitrosoureas or mitomycin C). Patients must be \>= 2 weeks since any prior administration of a study drug in a phase 0 or equivalent study and be \>= 1 week from palliative radiation therapy. Patients must have recovered to eligibility levels from prior toxicity or adverse events
* Patients who have had prior treatment with talazoparib are ineligible
* Patients who have had prior monoclonal antibody therapy must have completed that therapy \>= 6 weeks (or 3 half-lives of the antibody, whichever is shorter) prior to enrollment on protocol (minimum of 1 week between prior therapy and study enrollment) except for monoclonal antibody therapies that have been proven to be safe when combined with PARP inhibitor (PARPi) treatment (such as anti-PD-1/PD-L1 and anti-HER2), which must be completed \>= 4 weeks prior to enrollment
* Patients who are receiving any other investigational agents
* Patients with active brain metastases or carcinomatous meningitis are excluded from this clinical trial. Patients with treated brain metastases, whose brain metastatic disease has remained stable for \>= 1 month without requiring steroid and anti-seizure medication are eligible to participate
* Eligibility of subjects receiving any medications or substances with the potential to affect the activity or pharmacokinetics of talazoparib will be determined following review by the principal investigator
* 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
* Pregnant women are excluded from this study because the effects of the study drugs on the developing fetus are unknown
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* Patients who require use of coumarin-derivative anticoagulants such as warfarin are excluded. Low-dose warfarin (=\< 1 mg/day) is permitted
* Women who are currently lactating
* History of prior malignancies within the past 3 years other than non-melanomatous skin cancers that have been controlled