Nivolumab and Ibrutinib in Treating Patients With Relapsed, Refractory, or High-Risk Untreated Chronic Lymphocytic Leukemia, Small Lymphocytic Lymphoma, or Richter Transformation

Inclusion Criteria: * Patients will have a diagnosis of CLL or small lymphocytic lymphoma (SLL), refractory to or relapsed after at least one prior standard therapy or untreated with deletion (del)(17p) by fluorescence in-situ hybridization (FISH) (high-risk cytogenetics) and have an indication for treatment by IWCLL 2008 criteria (Cohort 1) OR have been on ibrutinib for at least 9 months with measurable persistent disease (absolute lymphocyte count \[ALC\] \> 4 K/muL, any lymph node \> 1.5 cm by computed tomography \[CT\] scan, or \> 30% lymphocytes on bone marrow aspirate differential) (Cohort 2), OR patients will have a diagnosis of RT, refractory to and/or relapsed after at least one prior standard therapy or untreated with del(17p) by FISH (high-risk cytogenetics) (Cohort 3) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Total bilirubin =\< 1.5 x upper limit of normal (ULN); for patients with Gilbert's disease, total bilirubin up to =\< 3 x ULN is allowed provided normal direct bilirubin * Serum creatinine =\< 1.5 x ULN * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN * Females of childbearing potential must have a negative serum or urine beta human chorionic gonadotrophin (beta-hCG) pregnancy test result within 24 hours prior to the first dose of treatment and must agree to use an effective contraception method during the study and for 23 weeks following the last dose of the study drugs; females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy; males who have partners of childbearing potential must agree to use an effective contraceptive method during the study and for 31 weeks following the last dose of study drugs * Patients or their legally authorized representative must provide written informed consent Exclusion Criteria: * History of another primary invasive malignancy that has not been definitively treated or in remission for at least 2 years; patients with non-melanoma skin cancers or with carcinomas in situ are eligible regardless of the time from diagnosis (including concomitant diagnoses); 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 * Any major surgery, radiotherapy, cytotoxic chemotherapy, biologic therapy, immunotherapy, immunomodulatory drugs, experimental therapy within 4 weeks prior to the first dose of the study drugs; Note: prior therapy with anti cluster of differentiation (CD)20 monoclonal antibody, anti CD52 monoclonal antibody, and lenalidomide are allowed; for oral targeted therapies (such as idelalisib, venetoclax), a washout of 3 days is allowed * 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 * History of stroke or cerebral hemorrhage within 2 month * Patients who have uncontrolled hypertension (defined as sustained systolic blood pressure \>= 160 mmHg or diastolic \>= 100 mmHg) * Known evidence of active cerebral/meningeal CLL; patients may have history of central nervous system (CNS) leukemic involvement if definitively treated with prior therapy and no evidence of active disease at the time of registration * Active, uncontrolled autoimmune hemolytic anemia or immune thrombocytopenia requiring steroid therapy * Patients with autoimmune diseases are excluded: patients with a history of inflammatory bowel disease (including Crohn's disease and ulcerative colitis) are excluded from this study as are patients with a history of autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis, systemic lupus erythematosus, Wegener's granulomatosis) * Patients with previous allogeneic stem cell transplant (SCT) within 6 months or with active acute or chronic graft-versus host disease are excluded; patients must be off immunosuppression for graft-versus host disease (GVHD) for at least 30 days before cycle 1 day 1 * Patients with organ allografts (such as renal transplant) are excluded * History of interstitial lung disease or pneumonitis * Patients who are on high dose steroid (\> 10 mg daily of prednisone or equivalent) or immune suppression medications; Note: patients on high-dose steroids (doses \> 10mg/day of prednisone or equivalent) or immune suppression medications are eligible provided these drugs are discontinued at least 3 days prior to starting on the study drugs * Patients with uncontrolled active infection (viral, bacterial, and fungal) are not eligible * Current or chronic hepatitis B or C infection, or known seropositivity for human immunodeficiency virus (HIV) * Patient is pregnant or breast-feeding * Concurrent use of investigational therapeutic agent * Malabsorption syndrome or other condition that precludes enteral route of administration * Concomitant use of warfarin or other vitamin K antagonists * Requires treatment with a strong cytochrome P450 (CYP) family 3, subfamily A (3A) inhibitor * 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