Ibrutinib With or Without Rituximab in Treating Patients With Relapsed Chronic Lymphocytic Leukemia

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)…