Akt Inhibitor MK2206, Bendamustine Hydrochloride, and Rituximab in Treating Patients With Relapsed Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria: * Diagnosis of chronic lymphocytic leukemia (CLL) according to the National Cancer Institute (NCI) criteria or small lymphocytic lymphoma (SLL) according to the World Health Organization (WHO) criteria; this includes previous documentation of: * Biopsy-proven SLL or * Diagnosis of CLL according to NCI working group criteria as evidenced by all of the following: * Peripheral blood B-cell count of \> 5 x 10\^9/L consisting of small to moderate size lymphocytes * Immunophenotyping consistent with CLL defined as: * The predominant population of lymphocytes share both B-cell antigens (CD19, CD20 \[typically dim expression\], or CD23) as well as CD5 in the absence of other pan-T-cell markers (CD3,CD2, etc.) * Clonality as evidenced by kappa (Κ) or lambda (λ) light chain expression (typically dim immunoglobulin expression) or other genetic method (e.g., immunoglobulin heavy chain variable \[IGHV\] analysis) * NOTE: splenomegaly, hepatomegaly, or lymphadenopathy are not required for the diagnosis of CLL * Before diagnosing CLL or SLL, mantle cell lymphoma must be excluded by demonstrating a negative fluorescence in situ hybridization (FISH) analysis for t (11;14) (IgH/CCND1) on peripheral blood or tissue biopsy, or negative immunohistochemical stains for cyclin D1 on involved tissue biopsy * Demonstrated progression after one or two prior lines of CLL therapy; note: rituximab monotherapy does not count as a prior line of therapy * Progressive disease with any one of the following characteristics based on standard criteria for treatment as defined by the NCI-Working Group (WG) 1996 * Symptomatic CLL characterized by any one of the following: * Weight loss \>= 10% within the previous 6 months * Extreme fatigue attributed to CLL * Fevers \> 100.5° Fahrenheit (F) for 2 weeks without evidence of infection * Drenching night sweats without evidence of infection * Evidence of progressive bone marrow failure with hemoglobin \< 11 g/dL or platelet count \< 100 x 10\^9/L * Massive or rapidly progressive splenomegaly (\> 6 cm below left costal margin) * Massive (\> 10 cm) or rapidly progressive lymphadenopathy * Life expectancy \>= 12 months * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) unless due to Gilbert's disease; if total bilirubin is \> 1.5 x ULN, a direct bilirubin should be performed and must be \< 1.5 mg/dL for Gilbert's to be diagnosed * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 2.5 ULN * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 times ULN * Creatinine =\< 1.5 times ULN OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels \> 1.5 x ULN * A non-transfused platelet count \>= 30 x 10\^9/L * Neutrophil count (absolute neutrophil count \[ANC\]) \>= 1 x 10\^9/L * Hemoglobin (Hgb) \>= 8 g/dL * Note: cytopenias due to bone marrow failure are common in patients with relapsed CLL requiring treatment; accordingly, normal bone marrow function is NOT required for participation * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Ability to complete patient diaries and questionnaire(s) by themselves or with assistance * Provide informed written consent * Willing to return to North Central Cancer Treatment Group (NCCTG) enrolling institution for follow-up * Willing to provide blood samples for correlative research purposes * Willing to provide bone marrow aspirate (body fluid) for correlative research purposes * MAYO ROCHESTER ONLY: willing to provide bone marrow core biopsy tissue for correlative research purposes * Willing to provide bone marrow biopsy for central pathology review (all patients) * Able to swallow whole tablets; NOTE: nasogastric or gastrostomy (G) tube administration is not allowed; tablets must not be crushed or chewed Exclusion Criteria: * Prior treatment with bendamustine * Prior treatment with any experimental Akt inhibitors * More than 2 previous purine nucleoside based-therapy (i.e. fludarabine, pentostatin, or cladribine) * More than 2 previous alkylating agent based-therapy (i.e. cyclophosphamide, chlorambucil) * More than 3 total prior lines of therapy for CLL * Primary refractory disease as defined by progression while receiving or within 6 months of completion of a chemoimmunotherapy regimen such as fludarabine, cyclophosphamide and rituximab (FCR) or pentostatin, cyclophosphamide and rituximab (PCR) * PHASE II ONLY: FISH abnormality of 17P deletions; (note: patients with 17P deletions will be included in Phase I but will be excluded in Phase II unless enough activity is found in the Phase I) * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens; including but not limited to the following: * New York Heart Association class III or IV heart disease * Recent myocardial infarction (\< 1 month) * Uncontrolled infection * Known infection with the human immunodeficiency virus (HIV/acquired immune deficiency syndrome \[AIDS\]) and/or patients taking highly active antiretroviral therapy (HAART) as further severe immunosuppression with this regimen may occur * Infection with known chronic, active hepatitis C * Positive serology for hepatitis B (HB) defined as a positive test for hepatitis B surface antigen (HBsAg); in addition, if negative for HBsAg but hepatitis B core antibody (HBcAb) positive (regardless of hepatitis B surface antibody \[HBsAb\] status), a HB deoxyribonucleic acid (DNA) test will be performed and if positive the subject will be excluded * Uncontrolled diabetes defined as hemoglobin A1c (HbA1c) \>= 8 or fasting blood glucose \>= 140 mg/dL * Any of the following: * History of significant ventricular arrhythmia in the last 5 years including: ventricular tachycardia or ventricular fibrillation * Corrected QT (QTc) prolongation on baseline electrocardiogram (ECG) (defined as a QTc interval \> 450 msec for males and QTc interval \> 470 msec for females) * Currently using a medication known to cause prolonged QTc which cannot be discontinued; note: other medications with possible risk of prolonged QTc are allowed but should be used with caution; patients using these medications should be monitored accordingly * Ventricular arrhythmia on baseline ECG (ventricular tachycardia or ventricular fibrillation \>= 3 beats in a row) * Second or third degree heart block * Receiving any other investigational agent concurrently which would be considered as a treatment for the primary neoplasm * Other active primary malignancy requiring treatment or which limits survival to \< 24 months * Any major surgery =\< 28 days prior to registration * Any radiation therapy =\< 4 weeks prior to registration * Current use of corticosteroids; EXCEPTION: low doses of steroids (\< 10 mg of prednisone or equivalent dose of other steroid) used for treatment of non-hematologic medical conditions; NOTE: previous use of corticosteroids is allowed * Active hemolytic anemia requiring immunosuppressive therapy or other pharmacologic treatment; NOTE: patients who have a positive Coombs test but no evidence of hemolysis are NOT excluded from participation * Receiving any medications or substances that are strong or moderate inhibitors of cytochrome P450 3A4 (CYP450 3A4); use of the following strong or moderate inhibitors are prohibited =\< 7 days prior to registration: * Strong inhibitors of CYP3A4 * Indinavir * Nelfinavir * Ritonavir * Clarithromycin * Itraconazole * Ketoconazole * Nefazodone * Saquinavir * Telithromycin * Moderate inhibitors of CYP3A4 * Aprepitant * Erythromycin * Fluconazole * Grapefruit juice * Verapamil * Diltiazem * Receiving any medications or substances that are inducers of CYP450 3A4; use of the following inducers is prohibited =\< 12 days prior to registration * Inducers of CYP3A4 * Efavirenz * Nevirapine * Carbamazepine * Modafinil * Phenobarbital * Phenytoin * Pioglitazone * Rifabutin * Rifampin * St. John's wort