Vorinostat, Fludarabine Phosphate, Cyclophosphamide, and Rituximab in Treating Patients With Previously Untreated Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria

• •Patients must have a confirmed diagnosis of CLL/SLL
• •Patients with previously untreated cluster of differentiation (CD)20+ CLL/SLL must have either Rai stage III/IV disease or be Rai stage I/II with evidence of disease activity as defined by the National Cancer Institute (NCI) 1996 guidelines; patients with SLL must be Stage III or IV per Ann Arbor staging system
• •Patient must have consented to participate in the study and signed and dated an appropriate institutional review board (IRB)-approved consent form that conforms to federal and institutional guidelines
• •Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2
• •Patient must have an anticipated (untreated) survival of at least 3 months
• •Female patient of childbearing potential has a negative serum pregnancy test beta-human chorionic gonadotropin (hCG) within 2 weeks prior to receiving the first dose of vorinostat
• •Female patient is either post menopausal, free from menses for \>= 2 years, surgically sterilized or willing to use 2 adequate barrier methods of contraception to prevent pregnancy or agrees to abstain from heterosexual activity throughout the study, starting with Visit 1
• •Male patients not sterilized must be willing to use adequate barrier methods of contraception to prevent pregnancy or agrees to abstain from heterosexual activity throughout the study, starting with Visit 1
• •Absolute Neutrophil Count (ANC) \>= 1,500/mcL
• •Platelets \>= 100,000/mcL
• •Hemoglobin \>= 9 g/dL
• •Prothrombin time or international normalized ratio (INR) =\< 1.5 upper limit of normal (ULN) unless receiving therapeutic anticoagulation
• •Partial thromboplastin time (PTT) =\< 1.2 times the ULN unless the patient is receiving therapeutic anticoagulation
• •Potassium level within normal limits
• •Magnesium level within normal limits
• •Serum creatinine =\< 1.5 x ULN OR if creatinine is \> 1.5 ULN the calculated creatinine clearance must be \>= 60 mL/min
• •Serum total bilirubin =\< 1.5 times ULN; patients with Gilbert's disease or similar syndrome involving slow conjugation of bilirubin are eligible with total bilirubin \> 1.5 times upper limit of normal; principal investigator (PI) review and approval required for anything above 2 times ULN
• •Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 ULN
• •Alkaline phosphatase =\< 2.5 ULN
• •Patients with cytopenias due to disease or pseudohyperkalemia that do not meet these criteria, will be considered eligible with review and approval by the PI or Co-PI prior to study entry
• •Patients with known human immunodeficiency virus (HIV) infection
• •Patients who are pregnant or nursing
• •Patients with known brain or leptomeningeal involvement by malignancy
• •Patients who have, in the opinion of the investigator, other medical, social, or psychosocial factors that may negatively impact compliance or their safety by participation in this study
• •Patient is currently participating or has participated in a study with an investigational compound or device within 30 days of initial dosing with study drugs(s)
• •Patient had prior treatment with an histone deacetylases (HDAC) inhibitor (e.g., romidepsin \[Depsipeptide\], NSC-630176, MS 275, LAQ-824, belinostat \[PXD-101\], LBH589, MGCD0103, CRA024781, etc); patients who have received compounds with HDAC inhibitor-like activity, such as valproic acid, as anti-tumor therapy should not enroll in this study; patients who have received such compounds for other indications, e.g. valproic acid for epilepsy, may enroll after a 30-day washout period
• •Patient with a history of a prior malignancy with the exception of cervical intraepithelial neoplasia; non-melanoma skin cancer; adequately treated localized prostate carcinoma with prostate-specific antigen (PSA) =\< 1.0; or who has undergone potentially curative therapy with no evidence of that disease for five years, and/or who is deemed at low risk for recurrence by his/her treating physician