Testing the Addition of the Anti-Cancer Drug Talazoparib to the Combination of Carboplatin and Paclitaxel for the Treatment of Advanced Cancer

Inclusion Criteria: * Patients must have histologically confirmed solid malignancy (excluding lymphoma) that is metastatic or unresectable and for which standard curative measures do not exist or are no longer effective, and for which: a) there is reasonable expectation of response to the combination of carboplatin/paclitaxel OR b) BRCA 1/2 germline mutation is present; due to the longstanding acceptance of BRCA 1 and 2 mutation testing through Myriad, results from Myriad will be acceptable; if testing for BRCA 1 and 2 germline mutations is done through another organization, a report from a genetics consult with a qualified medical professional confirming that the laboratory results show a recognized germline deleterious BRCA 1 or 2 mutation or rearrangement is required; if the latter cannot be obtained, principal investigator (PI) or study chair review of the lab results and confirmation of BRCA mutation or rearrangement will be required OR c) BRCA 1/2 somatic mutation previously identified using a Clinical Laboratory Improvement Amendments (CLIA) certified assay * Patients must have measurable or evaluable disease, as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 12 weeks * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 9 g/dL * Platelets \>= 150,000/mcL * Total bilirubin =\< 1.25 x institutional upper limit of normal (ULN), with the exception of \< 2.9 mg/dL for patients with Gilbert's disease * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN; =\< 5 x ULN in setting of metastatic liver disease * Creatinine =\< 1.5 x upper limit of normal OR creatinine clearance \>= 50 mL/min * Ability to take oral medications * Patients with central nervous system (CNS) metastases must be stable after therapy for CNS metastases (such as surgery, radiotherapy or stereotactic radiosurgery) for at least 4 weeks and must be off steroid treatment for 2 weeks prior to study enrollment * The effects of talazoparib (BMN 673) on the developing human fetus are unknown; for this reason and because 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 and for the duration of study participation; 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 4 months after completion of talazoparib (BMN 673) administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) or targeted therapies within 2 weeks prior to entering the study or those who have not recovered (=\< grade 1) from adverse events due to agents administered with the exception of any grade of alopecia * No prior carboplatin unless given in neoadjuvant/adjuvant setting for curative intent and more than 6 months have elapsed since last carboplatin dose; in the case of relapsed ovarian cancer, patients are eligible if more than 6 months have elapsed since last carboplatin dose * Patients who are receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to talazoparib (BMN 673) or other agents used in study * Peripheral neuropathy of severity greater than grade 1 * The following medications are contraindicated or must be used with caution; because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference * Contraindicated: * Cytochrome P450, family 2, subfamily C, polypeptide 8 (CYP2C8) strong and moderate inhibitors * CYP2C8 inducers * Cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) strong and moderate inhibitors * CYP3A4 inducers * CYP3A4 sensitive substrates * Exclusions: the following supportive care medications will be allowed will be allowed as they are routinely administered with carboplatin and paclitaxel and have no potential interaction with talazoparib (BMN 673): dexamethasone, aprepitant, fosaprepitant, and ondansetron); oral pain medications such as hydrocodone, oxycodone taken on an as needed basis are also permitted * Transdermal products designed for systemic delivery must be assessed for interaction potential; topical products not designed to provide systemic delivery (including inhaled products, ophthalmologic products and transvaginal preparations) do not need to be considered since they do not have appreciable systemic absorption * Other contraindicated medications (per above) are not allowed unless close monitoring with labs or drug levels or by symptoms with subsequent dose adjustments is feasible; patients taking these concurrent medications are ineligible unless they can discontinue or switched to alternative medications prior to initiation of the study drug (at least 5 half-lives) * Use with caution: * CYP2C8 sensitive substrates * CYP2C8 weak inhibitors * CYP3A4 non-sensitive substrates * CYP3A4 weak inhibitors * These agents may be permitted if discontinuation is not feasible and no acceptable alternatives are available as determined by the treating physician; however, caution should be used; consider monitoring with labs or drug levels or by symptoms and consider dose adjustments of the medication * 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 talazoparib (BMN 673) is a PARP inhibitor with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with talazoparib (BMN 673), breastfeeding should be discontinued if the mother is treated with talazoparib (BMN 673); these potential risks may also apply to other agents used in this study * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for interactions with study treatment; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * No clinically significant bleeding (i.e. gastrointestinal \[GI\] bleed, intracranial bleeding) within 6 months or major surgery within 4 weeks; minor surgeries (i.e. port placement, cataract surgery) are allowed within 2 weeks * Anticoagulation and anti-platelet therapies are not permitted (this includes coumadin, low molecular weight heparins, factor Xa inhibitors, aspirin and non-steroidal anti-inflammatory drug \[NSAIDS\] or other medicines with similar effects)