Testing the Combination of the Anti-cancer Drugs ZEN003694 (ZEN-3694) and Talazoparib in Patients With Advanced Solid Tumors, The ComBET Trial

Patients must have histologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective

Patients must have a tumor lesion that can be biopsied with 'low' or 'minimal' risk and at least one measurable disease site, as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1

* Note: Tumor lesions that are situated in a previously irradiated area may or may not be considered measurable

Patients in cohorts 1, 2, and 4 should have at least one relevant mutation. Patients enrolled in cohorts 1-3 do not require that PARP inhibitor (i) be the immediate prior therapy to be eligible for the trial. Patients should sign a screening consent that will allow the review of local next generation sequencing (NGS) or equivalent Clinical Laboratory Improvement Amendment (CLIA)-certified assay results by MD Anderson's Precision Oncology Decision Support (PODS) team to ensure that the mutations are actionable. No variants of uncertain significance (VUS) will be allowed

* Patients in Cohort 1 must have (i) a germline or somatic mutation in BRCA1 or BRCA2; and (ii) must have received prior PARPi monotherapy or PARPi combination-therapy

* Patients in Cohort 2 must have: (i) a germline or somatic mutation in any of the following deoxyribonucleic acid (DNA) damage response (DDR) genes: BARD1; FANCA; BRIP1; PALB2; RAD51; RAD51C; RAD51D, with no evidence of mutations in BRCA1 or BRCA2; and (ii) must have received prior PARPi monotherapy or PARPi combination therapy

* Patients in Cohort 3 must be (i) patients who have had PR/CR on prior PARPi monotherapy or PARPi combination treatment; and (ii) patients with no evidence of BRCA1 or BRCA2 mutations or any of the relevant DDR aberrations listed in cohort 2. Patients with ovarian cancer should not have progressed on platinum-therapy within six months of therapy

* Patients in Cohort 4 must have KRAS mutated advanced solid tumors. Prior treatments with KRAS inhibitors are permitted. Patients with KRAS G12C mutations must have already had KRAS G12C targeted therapy (e.g., sotorasib) previously

Patients must have received at least one line of systemic therapy in the advanced/metastatic setting. Subjects with diseases without known effective options, and subjects who have declined standard of care therapy prior to study introduction, are also eligible. Patients with ovarian cancer in cohort 3 should not have progressed on platinum within six months of therapy

Age \>= 18 years

* Because no dosing or adverse event data are currently available on the use of ZEN003694 (ZEN-3694) in combination with talazoparib in patients \< 18 years of age, children are excluded from this study

Patients must be greater than 4 weeks (6 weeks for nitrosoureas or mitomycin C) beyond treatment with any chemotherapy or other investigational therapy including 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. Patients must have recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities =\< grade 1) with the exception of alopecia or anorexia

Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)

Absolute neutrophil count \>= 1,500/mcL

Platelets \>= 150,000/mcL

Hemoglobin \>= 10.0 g/dL (no blood transfusions in the preceding 28 days)

Total bilirubin 1.5 x =\< institutional upper limit of normal (ULN) OR direct bilirubin = ULN for subjects with total bilirubin levels \> 1.5 x ULN

Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN

Creatinine 1.5 x =\< institutional ULN OR glomerular filtration rate (GFR) \>= 60 mL/min/1.73 m\^2 for subjects with creatinine levels \> 1.5 x institutional ULN, unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m\^2

Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial

Patients with evidence of chronic hepatitis B virus (HBV) infection must have an undetectable viral load while on suppressive therapy, if indicated

Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. However, patients with concurrent malignancy that is progressing or requiring active treatment are excluded

Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be of class 2B or better

The effects of the combination ZEN003694 (ZEN-3694) and talazoparib on the developing human fetus are unknown. For this reason, and because BET inhibitor agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 7 months after. 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

Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and for 7 months after completion of study drug administration

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)

Ability to understand and the willingness to sign a written informed consent document

What this study is about