Ofatumumab and Dinaciclib in Treating Patients With Relapsed or Refractory Chronic Lymphocytic Leukemia, Small Lymphocytic Lymphoma, or B-Cell Prolymphocytic Leukemia

Inclusion Criteria: * Patients must have histologically confirmed B-cell chronic lymphocytic leukemia (B-CLL)/small lymphocytic lymphoma (SLL) or a B-cell prolymphocytic leukemia (B-PLL) according to 2008 World Health Organization (WHO) diagnostic criteria * Patients must meet one or more of the following modified indications for treatment as described in the 2008 International Workshop on chronic lymphocytic leukemia (CLL) (IWCLL) guidelines for the diagnosis and treatment of CLL: * Progressive disease or marked splenomegaly and/or lymphadenopathy or disease requiring de-bulking for future allogeneic transplantation * Anemia (hemoglobin \< 11 mg/dL) or thrombocytopenia (platelets \< 100,000/μL) * Unexplained weight loss exceeding 10% of body weight over the preceding 6 months * Cancer Therapy Evaluation Program (CTEP) active version of the Common Terminology Criteria for Adverse Events (CTCAE) grade 2 or 3 fatigue * Fevers \> 100.5 º F or night sweats for greater than 2 weeks without evidence of infection * Progressive lymphocytosis, with an increase exceeding 50% over a 2-month period or a doubling time of less than 6 months * Need for cytoreduction prior to allogeneic stem cell transplant * Patients must have received at least one prior therapy that includes either fludarabine or equivalent nucleoside analogue, or an alternative regimen if there was a contraindication (i.e. autoimmune hemolytic anemia) or patient elected not to receive fludarabine * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy \>= 12 weeks * Absolute neutrophil count \>= 1,000/μL in absence of bone marrow involvement * Platelets \>= 30,000/μL in absence of bone marrow involvement * Total bilirubin =\< 1.5 X institutional upper limit of normal (ULN) unless secondary to Gilbert's * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal (ULN) unless due to infiltration of the liver * Creatinine =\< 2.0 mg/dL OR creatinine clearance \>= 50 mL/min/1.73 m\^2 for patients(Cockcroft-Gault estimated) * Patients with a history of current/previous infection with hepatitis B virus will be eligible if receiving appropriate antiviral prophylaxis * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier; corticosteroids alone will not be considered prior therapy, but must be discontinued at least 24 hours prior to the first day of therapy unless continued for indications other than the primary malignancy * Patients who are receiving any other investigational agents * Patients who have received prior treatment with dinaciclib will not be eligible; patients previously treated with ofatumumab will be eligible as long as their disease responded to previous treatment (defined as achieving at least stable disease by consensus criteria) and did not subsequently progress \< 3 months from completing treatment * Patients with known brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition as dinaciclib * History of anaphylactic reaction to rituximab or other anti-cluster of differentiation (CD)20 monoclonal antibody * Because dinaciclib is metabolized by the cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) liver enzyme, the eligibility of patients taking medications that are potent inducers or inhibitors of that enzyme will be determined following a review of their case by the principal investigator; every effort should be made to switch patients taking such agents or substances to other medications; any identified agent needs to be stopped at least 2 weeks prior to study registration; use of aprepitant will be permitted, however, based on drug-drug interaction study performed by the manufacturer showing no effect on dinaciclib pharmacokinetics (PK) * Patients with glucose-6-phosphate dehydrogenase (G6PD) deficiency are excluded * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant and/or breast-feeding women are excluded from this study; breastfeeding should be discontinued if the mother is treated with dinaciclib * Prior malignancy, except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer from which the subject is considered by his or her physician to have a 2 year survival expectation * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible