Venetoclax and Ibrutinib in Treating Patients With Chronic or Small Lymphocytic Leukemia

Inclusion Criteria: * Patients with a diagnosis of CLL/SLL: * Cohort 1: Refractory to and/or relapsed after at least one prior therapy will be eligible * Cohort 2: Untreated patients with high-risk features (del(17p), or mutated TP53, or del(11q), or unmutated IGHV, or \>= 65 years of age) are eligible (cohort 2) provided they have active disease requiring treatment as defined by the International Working Group for CLL (IWCLL) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Total bilirubin =\< 1.5 x upper limit of normal (ULN) or =\< 3 x ULN for patients with Gilbert's disease (in patients \[pts\] with elevated total bilirubin due to increased indirect bilirubin, pts with direct bilirubin =\< 1.5 x ULN are eligible) * Creatinine clearance \> 50 mL/min (calculated according to institutional standards or using Cockcroft-Gault, Modification of Diet in Renal Disease \[MDRD\], or Chronic Kidney Disease Epidemiology Collaboration \[CKD-EPI\] formula) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3.0 x ULN, unless clearly due to disease involvement * Platelet count of greater than 20,000/mul, with no platelet transfusion in 2 weeks prior to registration; this criteria is waived if the thrombocytopenia is due to bone marrow involvement with the disease * Women of childbearing potential must have a negative serum or urine beta human chorionic gonadotropin (beta-hCG) pregnancy test result within 7 days prior to the first dose of study drugs and must agree to use an effective contraception method during the study and for 30 days following the last dose of study drug; women of non- childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy; men who have partners of childbearing potential must agree to use an effective contraceptive method during the study and for 30 days following the last dose of study drug * Free of prior malignancies for 2 years with exception of patients diagnosed with basal cell or squamous cell carcinoma of the skin, or carcinoma "in situ" of the cervix or breast, who are eligible even if they are currently treated or have been treated and/or diagnosed in the past 2 years prior to study enrolment; if patients have another malignancy that was treated within the last 2 years, such patients may be enrolled if the likelihood of requiring systemic therapy for this other malignancy within 2 years is less than 10%, as determined by an expert in that particular malignancy at MD Anderson Cancer Center, and after consultation with the principal investigator * Patients or their legally authorized representative must provide written informed consent Exclusion Criteria: * Major surgery, radiotherapy, chemotherapy, biologic therapy, immunotherapy, investigational therapy within 3 weeks prior to the first dose of the study drugs * Uncontrolled active systemic infection (viral, bacterial, and fungal) * Known positive serology for human immunodeficiency virus (HIV), due to potential drug-drug interactions between anti-retroviral medications and the study drugs * Active hepatitis B infection (defined as the presence of detectable hepatitis B virus \[HBV\] deoxyribonucleic acid \[DNA\], hepatitis B e \[HBe\] antigen or hepatitis B surface \[HBs\] antigen); subjects with serologic evidence of prior vaccination (hepatitis B surface antigen \[HBsAg\] negative, anti-HBs antibody positive, anti-hepatitis B core \[HBc\] antibody negative) are eligible; patients who are HBsAg negative/hepatitis B surface antibody (HBsAb) positive but hepatitis B core antibody (HBcAb) positive are eligible, provided HBV DNA is negative * Active hepatitis C, defined by the detectable hepatitis C ribonucleic acid (RNA) in plasma by polymerase chain reaction (PCR) * Active, uncontrolled autoimmune phenomenon (autoimmune hemolytic anemia or immune thrombocytopenia) requiring steroid therapy with \> 20 mg daily of prednisone dose or equivalent * Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 2 months of screening, or any class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification * Patient is pregnant or breast-feeding * Concurrent use of warfarin * Received strong (CYP3A) inhibitors or strong CYP3A inducers within 7 days of starting study drugs * Consumed grapefruit, grapefruit products, Seville oranges, or star fruit within 7 days of starting study drugs * Prior treatment with venetoclax or ibrutinib * Malabsorption syndrome or other condition that precludes enteral route of administration * Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that in the opinion of the investigator may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and/or would make the patient inappropriate for enrollment into this study