Veliparib in Combination With Carboplatin and Paclitaxel in Treating Patients With Locally Advanced or Metastatic Solid Tumors

Inclusion Criteria: * Histologically or cytologically confirmed solid tumor that has evidence of metastatic spread (stage IV) or is locally advanced and unresectable * Patients with breast cancer may have estrogen receptor positive or negative (ER+ or ER-) disease * Patients with breast cancer may not be human epidermal growth receptor -2 (HER2)-positive ( 3+), or fluorescent in situ hybridization (FISH) ratio \> 2.2 * Patients in the biopsy expansion cohort must have "triple negative" breast cancer defined as: * Estrogen receptor staining \< 10%; progesterone receptor staining \<10%; Her 2 \< 2.2 by FISH, or immunohistochemistry (IHC) 0-2+ * Patients may have been previously treated * In the dose escalation cohort, there is no limit to prior therapies * In the expansion cohort, patients may have only had 1-3 prior regimens for metastatic disease * Patients may have received prior carboplatin, paclitaxel, or poly (ADP-ribose) polymerase (PARP) inhibitor therapy as part of their previous treatment regimens * However, patients may NOT have received prior therapy with paclitaxel, carboplatin, and PARP inhibitor in combination * Patients must not have received chemotherapy within 4 weeks of starting study (or 6 weeks if prior treatment was with carmustine \[BCNU\] or mitomycin C) * Patients must not have received radiation within 2 weeks of starting study * Eastern Cooperative Oncology Group (ECOG) performance status (PS)\< 2 (Karnofsky \> 60%) * Life expectancy \> 2 months * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelet count \>= 100,000/mcL * Total bilirubin =\< 1.5 times upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 times ULN * Creatinine normal within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73m\^2 for patients with creatinine levels above institutional normal * Must able to swallow pills * Pregnant women are excluded from this study * 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 participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Patients enrolled in the expanded cohort with mandatory biopsies must: * Have accessible tumors * Not be on therapeutic anticoagulation * Have signed informed consent form Exclusion Criteria: * Patients who have had chemotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) or radiotherapy within 2 weeks (4 weeks for central nervous system \[CNS\] metastases) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients may not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to veliparib or other agents used in study * Concurrent treatment with bisphosphonates, or other bone anti-resorptive agent such as denosumab is allowed; concurrent treatment with hormonal therapy (tamoxifen, ovarian suppression with gonadotropin-releasing hormone \[GNRH\] agonists, aromatase inhibitors) or trastuzumab therapy is NOT allowed in breast cancer patients; prostate cancer patients may continue GNRH agents * 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; breastfeeding should be discontinued if the mother is treated with veliparib * Active seizure or history of seizure disorder * Patients with CNS metastases must be stable after therapy for CNS metastases (such as surgery, radiotherapy or stereotactic radiosurgery) for \> 3 months and must be off steroid treatment prior to study enrollment * Patients who undergo biopsy as part of the study in the expanded dose cohort should not be on anti-coagulants or have a pre-existing coagulopathy * Peripheral neuropathy of severity greater than grade 1