Veliparib, Cyclophosphamide, and Doxorubicin Hydrochloride in Treating Patients With Metastatic or Unresectable Solid Tumors or Non-Hodgkin Lymphoma

Inclusion Criteria: * 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 with either solid tumors or non-Hodgkin's lymphoma are eligible * At the recommended Phase II dose level, an additional 6 to 12 patients in each group with the following criteria will be enrolled: documented breast cancer (BRCA)1/BRC2 mutation, triple-negative breast cancer defined as estrogen receptor (ER)-negative, progesterone receptor (PR)-negative, and human epidermal growth factor receptor (HER)2-negative, or patients who would benefit from a cyclophosphamide-based regimen * On the schedule of ABT-888 given for 7 or 14 days, only patients with metastatic breast cancer will be enrolled * Patients must be \>= 4 weeks since prior chemotherapy or radiation therapy (\>= 6 weeks if the last regimen included carmustine \[BCNU\] or mitomycin C); patients previously treated with cyclophosphamide should not be necessarily excluded * Patients with non-Hodgkin's lymphoma that is amenable to hematopoietic stem cell transplantation with curative intent may participate only if stem cell transplant is refused or is not indicated * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Life expectancy of greater than 2 months * Hemoglobin \>= 9.0 g/dL * Absolute neutrophil count (ANC) \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) or alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal (ULN), =\< 5 x ULN if known hepatic metastases * Creatinine within normal institutional limits OR creatinine clearance \>= 60 ml/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Prothrombin time (PT)/international normalized ratio (INR)/partial thromboplastin time (PTT) =\< 1.2 X institutional ULN * 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 * Patients enrolled in a group where the treatment is adriamycin and cycloblastin (AC): ejection fraction \>= 50% by multigated acquisition scan (MUGA) or echocardiogram * Patients must sign informed consent Exclusion Criteria: * Concurrent administration of any other investigational agent(s) * Prior high-dose therapy requiring hematopoietic stem cell transplantation * Prior anti-cancer treatments involving radioactive pharmaceuticals * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ABT-888 and/or cyclophosphamide * Patients receiving any medications or substances that are strong inhibitors or strong inducers of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP 3A4), cytochrome P450, family 2, subfamily B, polypeptide 6 (2B6), cytochrome P450, family 2, subfamily C, polypeptide 9 (2C9) or cytochrome P450, family 2, subfamily C, polypeptide 19 (2C19) are prohibited; at the time of screening, if the patient is currently receiving any of the listed prohibited medication(s), the medication(s) must be discontinued for a period of no less than 7 days prior to administration of the first dose of study medication in order for the patient to meet study eligibility except for the following substance where the washout should be 6 months: amiodarone * 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; New York Heart Association (NYHA) grade II or greater congestive heart failure * 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; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated; NOTE: HIV seropositive patients not receiving combination antiretroviral therapy who have cluster of differentiation (CD)4 cells \>= 350/mm\^3, no opportunistic infections and meet all eligibility criteria may participate in this study * Any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease) that impairs their ability to swallow and retain ABT-888 capsules * Patients with gastrointestinal conditions that might predispose for drug intolerability or poor drug absorption (e.g., inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, malabsorption syndrome, active peptic ulcer disease) are excluded; subjects with ulcerative colitis, inflammatory bowel disease, or a partial or complete small bowel obstruction are also excluded * Patients with active central nervous system (CNS) metastases are excluded * Patients with CNS metastases that have been treated must be off steroid treatment for \> 3 months, be asymptomatic and off steroid treatment prior to study enrollment * Patients that have symptoms to suggest CNS metastases should have a brain magnetic resonance imaging (MRI) within 28 days of enrollment to confirm the absence of CNS metastases; contrast computed tomography (CT) is acceptable for patients who are unable to undergo a brain MRI * Patients with active seizure or a history of active seizure * Any other medical, social, or psychological condition that may significantly affect safety and/or compliance * Patients enrolled in a group where treatment is AC: prior doxorubicin exposure of \> 300 mg/m\^2 or equivalent anthracycline exposure (i.e., epirubicin dose \> 540 mg/m\^2)