Phase I/Ib Study of Nivolumab & Veliparib in Patients With Advanced Solid Tumors & Lymphoma

Inclusion Criteria: * Patients must have a histologically documented (either primary or metastatic site) diagnosis of advanced solid tumor cancer (stage IV or unresectable) or aggressive lymphoma (diffuse large B cell lymphoma, mantle cell lymphoma, T cell lymphoma, and natural killer \[NK\] cell lymphoma) * NOTE: The following histologies will be excluded given known response to PD-1/PD-L1 inhibitor monotherapy: non-small cell lung cancer, squamous cell carcinoma of head and neck, melanoma, renal cell carcinoma, bladder cancer, Hodgkin's lymphoma, Merkel cell carcinoma, and high-frequency microsatellite instability (MSI-H) colorectal cancer * All patients must have received, and be relapsed/refractory to at least one line of systemic therapy * NOTE: This does not include surgery or radiation alone; patients may have received any number of systemic therapies * All patients with relapsed/refractory lymphoma must have received or be ineligible for autologous stem cell transplant or be ineligible for allogeneic stem cell transplant * NOTE: Patients must not have had a prior allogeneic stem cell transplant * Patients must have measurable disease as per appropriate guidelines: * Solid tumors: by RECIST v1.1 * Lymphoma: patient has at least one measurable nodal lesion (\>= 2 cm) according to Lugano classification; if the patient has no measurable nodal lesions \>= 2 cm in the long axis at screening, then the patient must have at least one measurable extra-nodal lesion * Patients must have the ability to understand and the willingness to sign a written consent prior to registration in the study * For expansion cohort patients, the profiling must reveal at least one mutation in the following selected DNA repair genes involved in cell cycle arrest signal transduction, BRCA1 pathway, Fanconi's proteins pathway, and RAD51 pathway: (ATR, ATM, CHEK1, CHEK2, BRCA1, BAP1, BARD1, FANCD2, FANCE, FANCC, RAD50, FANCA, RAD51, BRCA2, PALB2, CDK12 \[ENSG00000167258, also known as CRK7, CRKR, CRKRS\], POLE, POLD1, BRAC2, PRKDC, ERCC2, POLQ, MRE11A, NBN \[MBS1\]), or at least one gene amplification in FANCD2, FANCE, FANCC, FANCA, C11orf30 (EMSY) * NOTE: Tissue or blood cell free DNA are allowed for genomic profiling of tumor; profiling should have been performed at a Clinical Laboratory Improvement Act (CLIA) certified lab =\< 1 year prior to registration * NOTE: Patients in the dose escalation phase are not required to have such mutations; although genomic profiling is not required for dose escalation patients, it is encouraged in these patients prior to or after study registration if feasible * Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * Patients must have adequate organ and bone marrow function =\< 14 days prior to registration, as defined below (Note: blood transfusion or growth factors is not permitted within 14 days of registration): * Absolute neutrophil count \>= 1.5 x 10\^9/L * Hemoglobin \>= 9 g/dL * Platelets \>= 100 x 10\^9/L * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Alanine aminotransferase and aspartate aminotransferase =\< 5 x ULN * Calculated creatinine clearance according to the Cockcroft and Gault equation \>= 50 mL/min * Females of child-bearing potential (FOCBP) and men who are sexually active with FOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment and the designated post-treatment period * NOTE: A FOCBP is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy * Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months) * FOCBP must have a negative pregnancy test =\< 7 days prior to registration * Patients must be able to swallow oral medication Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy =\< 14 days prior to entering the study are not eligible * NOTE: Patients may not have had systemic chemotherapy within 28 days * Patients are not eligible who have had major surgery =\< 14 days of registration; please contact principle investigator (PI) and quality assurance monitor (QAM) for questions about specific surgical procedures * Patients are not eligible who have received prior PARP inhibitors (including but not limited to veliparib, talazoparib, rucaparib, and olaparib) * Patients are not eligible who have received systemic chemotherapy or investigational agents =\< 28 days prior to registration * Patients are not eligible who have received prior immunotherapy including interleukin-2 and immune checkpoint antagonists and/or agonists (including but not limited to PD-1, PD-L1, CD137, or OX40) * NOTE: Single agent anti-CTLA4 monoclonal antibody treatments are permitted; cancer vaccine therapies are permitted * Patients with the following histologies are not eligible for either study cohort given known response to PD-1/PD-L1 inhibitor monotherapy: * Non-small cell lung cancer, squamous cell carcinoma of head and neck, melanoma, renal cell carcinoma, bladder cancer, Hodgkin's lymphoma, Merkel cell carcinoma, and MSI-H colorectal cancer * Patients are not eligible who have had a prior allogeneic stem cell transplant * NOTE: Autologous stem cell transplant is acceptable * Patients who are taking any herbal (alternative) medicines are NOT eligible for participation; patients must be off any such medications by the time of registration for \>= 14 days * NOTE: Vitamin supplements are acceptable * Patients must have no history of central nervous system (CNS) metastasis at the screening assessment * NOTE: Patients with stable brain metastases (mets) which have been treated are eligible; patients with suspected symptoms of CNS metastasis should undergo CNS imaging at the time of screening to rule out active metastasis * Patients who have had a prior severe infusion reaction to a monoclonal antibody are not eligible * Patients are not eligible who have a history of or active autoimmune disease within the past 3 years with the following exceptions: * Vitiligo or alopecia * Hypothyroidism on stable doses of thyroid replacement therapy * Psoriasis not requiring systemic therapy within the past 3 years * Patients with a history of primary immunodeficiency disease or tuberculosis are not eligible * Patients who have an uncontrolled current illness including, but not limited to any of the following, are not eligible: * Uncontrolled pulmonary, renal, or hepatic dysfunction * Ongoing or active infection requiring systemic treatment including hepatitis B and hepatitis C * Known active or chronic viral hepatitis or human immunodeficiency virus (HIV) * Psychiatric illness/social situations that would limit compliance with study requirements * Clinically significant gastrointestinal disease or digestive dysfunction compromising absorption of veliparib * Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints * Female patients who are pregnant or nursing are not eligible * Patients with a prior diagnosis of cancer must not have received treatment in the last 3 years prior to registration * NOTE: Patients with a history of completely resected non-melanomatous skin carcinoma or successfully treated in situ carcinoma are eligible * Patients must not have a history of prior stroke, transient ischemic attack (TIA), pulmonary embolism, or untreated deep vein thrombosis * NOTE: Patients may be eligible if they have received at least 3 months of anticoagulation for a deep vein thrombosis