Venetoclax and Ibrutinib in Treating in Participants With Chronic Lymphocytic Leukemia and Ibrutinib Resistance Mutations

Inclusion Criteria: * Diagnosis of chronic lymphocytic leukemia (CLL) meeting criteria established in the World Health Organization (WHO) classification of hematologic disorders or International Workshop on Chronic Lymphocytic Leukemia (IWCLL) * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 * Currently taking ibrutinib and first took ibrutinib \> 3 months ago * Presence of a known ibrutinib resistance mutation at ≥ 4% variant allele frequency OR \< 4% with two separate measurements at least 4 weeks apart with increasing variant allele frequency * Adequate bone marrow function independent of growth factor support at screening unless clearly due to marrow involvement by CLL and/or disease-related immune thrombocytopenia; if cytopenias are due to disease in the bone marrow any degree of cytopenias are allowed; patients with active uncontrolled autoimmune cytopenias are excluded * Hemoglobin ≥ 8 g/dL * Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 * Platelets ≥ 40,000/mm\^3 * Prothrombin time/partial thromboplastin time (PT/PTT) ≤ 1.5 x upper limit of normal (ULN) (unless receiving anticoagulation) * Total bilirubin ≤ 1.5 x ULN (excepting Gilbert's syndrome) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 ≤ ULN * Creatinine clearance ≥ 40 mL/min/1.73m\^2 * Using 24-hour creatinine clearance or modified Cockcroft-Gault equation * All patients must practice a highly effective method of birth control * Able to take an absorb pill form oral medications * Ability to understand and sign a written informed consent Exclusion Criteria: * Inability to continue taking ibrutinib for any reason * Treatment with chemotherapy, immunotherapy, radiotherapy, targeted small molecule inhibitors, biologic agents, and/or an investigational therapy for 5 half-lives prior to first study dose of venetoclax; treatment with a biologic agent, such as a monoclonal antibody, for 30 days prior to study treatment; treatment with ibrutinib is allowed * Need for anticoagulation with a vitamin K antagonist (warfarin); other anticoagulants and antiplatelet agents are allowed * Treatment with a moderate or strong cytochrome P450 3A4 (CYP3A) inhibitor or inducer within 7 days prior to first dose of venetoclax or need for treatment with a strong CYP3A inhibitor or inducer during the period or the study; patients who have a need for treatment with a moderate CYP3A inhibitor or inducer during venetoclax dose escalation will also be excluded * Uncontrolled autoimmune hemolytic anemia or thrombocytopenia * History of lymphoma (Richter's syndrome) unless in complete remission \> 2 years without relapse * Known active involvement of the central nervous system by lymphoma or leukemia * Known infection with the human immunodeficiency (HIV) virus * A cardiovascular disability status of New York Heart Association Class ≥ 2, defined as cardiac disease in which patients are comfortable at rest but ordinary physical activity results in fatigue, palpitations, dyspnea, or angina pain * Positive hepatitis serology: * Patients with positive serology for hepatitis B defined as positivity for hepatitis B virus surface antigen measurement (HBsAg) or anti-hepatitis B core total antibodies (antiHBc) may be considered for inclusion in the study on a case-by-case basis if they are hepatitis B viral deoxyribonucleic acid (DNA) negative and are willing to undergo ongoing hepatitis B virus (HBV) DNA testing by real-time polymerase chain reaction (PCR) monthly during the study * Patients with positive hepatitis B surface antigen (HBsAg) consistent with prior vaccination to HBV (i.e., hepatitis B immune status/anti-hepatitis B surface antibody \[anti-HBs+\], anti-HBc-) may participate * Patients suspected to have false positive serologic studies because of intravenous (IV) immunoglobulin administration are potentially eligible without need for further monitoring if they have negative PCR studies for viral DNA/RNA after discussion with the principal investigator * Patients with positive hepatitis C serology are excluded unless they have negative hepatitis C virus (HCV) ribonucleic acid (RNA) testing after receiving HCV-specific treatment and the case is discussed with the principal investigator * Female patients who are pregnant, breast-feeding, or planning to become pregnant * 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 * History of active malignancies other than chronic lymphocytic leukemia (CLL) within the past 3 years prior to study entry, with the exception of: * Adequately treated in situ carcinoma or the cervix or breast * Basal cell or localized squamous cell carcinoma of the skin * Previous malignancy treated with curative therapy and not expected to relapse * Inability to swallow capsules or tablets, or disease significantly affecting gastrointestinal function and/or inhibiting small intestine absorption (malabsorption syndrome, resection of the small bowel, poorly controlled inflammatory bowel disease, etc.) * Prior allogeneic stem cell transplant with day 0 \< 12 months prior and/or with chronic graft versus host disease (GVHD) requiring current use of immunosuppression; patients with prior allogeneic stem cell transplant with day 0 \> 12 months prior who do not require immunosuppression for GVHD will be eligible