Veliparib With or Without Mitomycin C in Treating Patients With Metastatic, Unresectable, or Recurrent Solid Tumors

Inclusion Criteria: * Patients must have a histologically confirmed solid malignancy that is metastatic, or unresectable, or recurrent, for which no curative or standard of care exist, or this standard of care is no longer effective * Tumors have been shown to be deficient for the FA pathway, based on Fanconi anemia triple stain immunofluorescence (FATSI) screening * Patients will be consented to have their existing, or about to be obtained, paraffin embedded tumor tissue screened for FA deficiency; screening will be performed on an ongoing basis on the breast, thoracic, gastrointestinal (GI), Georgetown University (GU), and gynecologic (GYN) Ohio State University (OSU) clinics, anteceding and concurrently with the clinical trial; it will continue until the numbers of patients required for the clinical trial are identified and enrolled; based on the estimation from our preliminary data of 15 to 30% of patients, depending on the primary organ site, having tumors deficient for the FA pathway we will need to screen around 300 patients' samples to identify 40-50 patients; none of the eligibility criteria defined above or below will need to be met for the screening portion, since FA deficient patients identified by screening may meet eligibility criteria for the clinical trial at a later time; (e.g., patient is undergoing standard of care treatment at the time of the screening); separate written consents for screening and for the clinical trial will be obtained from patients * Up to two chemotherapy regimens for metastatic disease are allowed; in addition, prior adjuvant/neo-adjuvant chemotherapy, hormonal therapy, molecular targeted therapy or estrogen receptor B (Erb) inhibitor treatments (e.g., erlotinib, Herceptin, sorafenib, sunitinib) will be allowed and will not count towards eligibility; at least 4 weeks must elapse since prior chemotherapy or radiation therapy (two weeks for erlotinib, hormonal therapy, or limited field palliative radiation to bone, brain, or radiosurgery), 6 weeks if the last regimen included nitrosoureas or mitomycin C; previous use of mitomycin C would be restricted to topical applications (bladder cancer) or chemoembolization (e.g., liver tumors) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 3 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count (ANC) \>= 1,500/mcL * Hemoglobin \>= 9 g/dL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limit * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * 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 should be able to swallow capsules * EXPANSION COHORT: * Diagnosis of colorectal malignancy * Absence of Fanconi anemia, complementation group D2 (FANCD2) foci by FATSI screening * Presence of biopsiable lesion by imaging * Consent to a baseline (prior to treatment) tumor biopsy and for a repeat biopsy at the time of progression on the event that an antitumor response is demonstrated on the MMC-ABT-888 regimen * Same eligibility as above, except that they will have no limitations related prior number of chemotherapy regimens given; patients could have received prior treatment with PARP inhibitors if used as single agent Exclusion Criteria: * Patients may not be receiving any other investigational agents * Patients with known central nervous system (CNS) metastases (unless previously resected or irradiated and not clinically active); patients with CNS metastases must be stable after therapy for \> 3 months and off steroid treatment prior to study enrollment * History of allergic reactions attributed to compounds of similar chemical or biologic composition as ABT-888 or Mitomycin C * 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 * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients with active seizure or a history of seizures * Patients previously treated with PARP inhibitors; with the exception of patients enrolled on Arm 2 who may have had prior treatment with PARP inhibitors as monotherapy