Ibrutinib in Treating Minimal Residual Disease in Patients With Chronic Lymphocytic Leukemia After Front-Line Therapy

Inclusion Criteria: * Understand and voluntarily sign an informed consent form * Able to adhere to the study visit schedule and other protocol requirements including willing to provide blood, baseline bone marrow aspirate, and control deoxyribonucleic acid (DNA) samples for correlative research purposes * Diagnosis of B-cell chronic lymphocytic leukemia (B-CLL), confirmed by flow cytometry and as per the criteria outlined by the IWCLL/Hallek December 2008 * Prior frontline therapy for B-CLL must have been discontinued \>= 56 days but =\< 365 days prior to registration; NOTE: Patients on supportive care therapy due to use of specific induction regimen such as antibiotics may continue on those treatments at the discretion of the treating physician * Patient must have completed a frontline induction therapy (minimum of 2 treatment cycles); NOTE: Standard therapies/therapeutic agents are defined as those listed in the National Comprehensive Cancer Network (NCCN) guidelines for treatment of CLL; also, patients who received induction regimen as part of a clinical trial and is not necessarily mentioned in the NCCN guidelines, will also be eligible as long as the patient has completed at least 2 treatment cycles of induction regimen, achieved a clinical response (PR or CR) and is able to meet all other criteria for the study; however, patients who have previously received ibrutinib or have been randomized to ibrutinib containing arms in a clinical trial will not be eligible for this…