Veliparib, Paclitaxel, and Carboplatin in Treating Patients With Solid Tumors That Are Metastatic or Cannot Be Removed by Surgery and Liver or Kidney Dysfunction

Inclusion Criteria: * Patients must have histologically confirmed malignancy that is radiologically evaluable and metastatic or unresectable, for which standard curative or palliative measures do not exist or are no longer effective, and for which there is expectation of response to the combination of carboplatin/paclitaxel (i.e., lung, ovarian, breast, melanoma, head and neck, endometrial, urothelial, testicular, esophageal, carcinoma of unknown primary); for indications not listed, eligibility based on disease must be verified by the principal investigator before they are considered * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 12 weeks * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 8.0 g/dL * Patients with all degrees of renal dysfunction are allowed including patients on hemodialysis; patients with mild to severe hepatic dysfunction are allowed as defined below: * Total bilirubin =\< 5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 10 x ULN * For patients with a recently placed biliary stent, patients should have consistent results within a hepatic group from two laboratory readings within 3 days apart, taken at least 10 days following biliary stent placement; for patients with a biliary stent placed over 2 months ago, no obstruction or blockage can have occurred within the last 2 months * 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 Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those whose adverse event due to agents administered more than 4 weeks earlier have not resolved or stabilized; patients who have been administered ABT-888 as part of a single or combination, phase 0 or I study, should not necessarily be excluded from participating in this study solely because of receiving prior ABT-888 * Patients may not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ABT-888 or other agents used in study * Peripheral neuropathy of severity greater than grade 1 * Inability to take oral medications on a continuous basis * Evidence of bleeding diathesis * 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 3 months and must be off steroid treatment prior to study enrollment * 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 ABT-888; 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; however, HIV-positive patients without an acquired immune deficiency syndrome (AIDS)-defining diagnosis who are not receiving agents with the potential for pharmacokinetic (PK) interactions with ABT-888 may be eligible * Patients with both hepatic and renal dysfunction will also be excluded * Patients who received and progressed on the combination of carboplatin/paclitaxel will not be eligible * Active seizure or history of seizure disorder