Could adding an antibody boost a standard CLL drug?

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Patients must have a diagnosis of CLL/small lymphocytic lymphoma (SLL) or prolymphocytic leukemia (PLL) and be previously treated; given the poor outcome of CLL/SLL/PLL patients with 17p deletion (del) or tumor protein (TP)53 mutation to standard frontline chemo-immunotherapy, such patients will be eligible if they are untreated * Patients must have an indication for treatment by 2008 International Workshop on Chronic Lymphocytic Leukemia (IWCLL) criteria * Patients must be age \>= 18 years at the time of signing informed consent, understand and voluntarily sign an informed consent, and be able to comply with study procedures and follow-up examinations * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Patients of childbearing potential must be willing to practice highly effective birth control (e.g., condoms, implants, injectables, combined oral contraceptives, intrauterine devices \[IUDs\], sexual abstinence, or sterilized partner) during the study and for 30 days after the last dose of study drug; women of childbearing potential include any female who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or is not postmenopausal * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) except for patients with bilirubin elevation due to Gilbert's disease who will be allowed to participate * Alanine aminotransferase (ALT) =\< 2.5 x ULN * Estimated creatinine clearance (CrCl) of \> 30 mL/min, as calculated by the Cockcroft-Gault equation unless disease related * Free of prior malignancies for 3 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 3 years prior to study enrollment; if patients have another malignancy that was treated within the last 3 years, such patients can be enrolled, after consultation with the principal investigator, 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 * A urine pregnancy test (within 7 days of enrollment date) is required for women with childbearing potential Exclusion Criteria: * Pregnant or breast-feeding females * Prior therapy with ibrutinib or other kinase inhibitors that target Bruton's tyrosine kinase (BTK); patients who previously received therapy with the phosphoinositide-3 kinase (PI3K) delta inhibitor idelalisib (Zydelig) are allowed to be enrolled * Treatment including chemotherapy, chemo-immunotherapy, monoclonal antibody therapy, radiotherapy, high-dose corticosteroid therapy (more than 60 mg prednisone daily or equivalent), or immunotherapy within 21 days prior to enrollment or concurrent with this trial * Investigational agent received within 30 days prior to the first dose of study drug * Systemic fungal, bacterial, viral, or other infection not controlled (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment) * Patients with uncontrolled autoimmune hemolytic anemia (AIHA) or autoimmune thrombocytopenia (ITP) * Patients with severe hematopoietic insufficiency, as defined by an absolute neutrophil count of less than 500/uL, unless disease-related, and/or a platelet count of less than 30,000/uL at time of screening for this protocol * Any other severe concurrent disease, or have a history of serious organ dysfunction or disease involving the heart, kidney, liver or other organ system that may place the patient at undue risk to undergo therapy with ibrutinib and rituximab * Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 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 6 months * Evidence of bleeding diathesis or coagulopathy within 3 months * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to enrollment date, anticipation of need for major surgical procedure during the course of the study * Minor surgical procedures, fine needle aspirations or core biopsies within 7 days prior to enrollment date; bone marrow aspiration and/or biopsy are allowed * Serious, non-healing wound, ulcer, or bone fracture * Treatment with Coumadin; patients who recently received Coumadin must be off Coumadin for at least 7 days prior to start of the study