Metformin Hydrochloride and Ritonavir in Treating Patients With Relapsed or Refractory Multiple Myeloma or Chronic Lymphocytic Leukemia

Inclusion Criteria: * All subjects must have the ability to understand and the willingness to sign a written informed consent * Life expectancy of \> 3 months * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 FOR PATIENTS WITH MULTIPLE MYELOMA (MM): * Diagnosis of multiple myeloma * Patients with MM must have measurable disease, defined as one or more of the following: * Serum M-protein \>= 0.5 g/dL * Urine M-protein \>= 200 mg/24 hr * Serum immunoglobulin free light chain (FLC) \>= 100 mg/L (10 mg/dL) and abnormal serum immunoglobulin kappa to lambda FLC ratio * IgA patients must have serum quantitative immunoglobulin \>= 750 mg/dL * Patients with oligosecretory or non-secretory disease must have a documented abnormal free light chain ratio (normal value 0.26 to 1.65) or a value beyond the laboratory calculation range * Disease must be refractory or relapsed after \>= 3 prior regimens (induction therapy and stem cell transplant +/- maintenance will be considered as one regimen) FOR PATIENTS WITH CHRONIC LYMPHOCYTIC LEUKEMIA (CLL): * Diagnosis of CLL without the following: Richter's transformation, prolymphocytic leukemia (PLL), small lymphocytic lymphoma (SLL) * Measurable disease, defined as one or more of the following: * Lymphocytosis \>= 5000 in peripheral blood * Measurable lymph nodes \> 1.5 cm on palpation and/or computed tomography (CT) scan * Organomegaly by physical exam and/or CT scan * Active disease per International Workshop on Chronic Lymphocytic (IWCLL) 2008 criteria, as defined as one of the following: * Evidence of progressive marrow failure as manifested by the development of, or worsening of, anemia and/or thrombocytopenia * Massive (i.e., at least 6 cm below the left costal margin) or progressive or symptomatic splenomegaly * Massive nodes (i.e., at least 10 cm in longest diameter) or progressive or symptomatic lymphadenopathy * Progressive lymphocytosis with an increase of more than 50 percent over a two-month period or lymphocyte doubling time (LDT) of less than six months; LDT can be obtained by linear regression extrapolation of absolute lymphocyte counts obtained at intervals of two weeks over an observation period of two to three months; in patients with initial blood lymphocyte counts of less than 30 x 10\^9/L (30,000/L), LDT should not be used as a single parameter to define a treatment indication; in addition, factors contributing to lymphocytosis or lymphadenopathy other than CLL (e.g., infection) should be excluded * Autoimmune anemia and/or thrombocytopenia that is poorly responsive to corticosteroids or other standard therapy * Constitutional symptoms, defined as any one or more of the following disease-related symptoms or signs: * Unintentional weight loss of 10 percent or more within the previous six months * Significant fatigue (i.e., ECOG performance scale \[PS\] 2 or worse; inability to work or perform usual activities) * Fevers higher than 100.5 degrees Fahrenheit (F) or 38.0 degrees Celsius (C) for two or more weeks without other evidence of infection * Night sweats for more than one month without evidence of infection * Received at least 2 prior therapies (regimens) for CLL * In the opinion of the investigator do not require rapid cytoreduction due to bulky disease (e.g. painful lymphadenopathy or organomegaly, or impending end-organ dysfunction * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 * Platelets \>= 50,000/mm\^3 * Aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) =\< 3 x ULN * Total bilirubin =\< 1.5 x ULN; unless presence of Gilbert's syndrome, liver involvement by CLL or MM, or stable chronic liver disease per investigator's assessment * Creatinine clearance of \>= 45 mL/min per 24 hour urine collection or the Cockcroft-Gault formula * Woman of childbearing potential (WOCBP): negative urine or serum pregnancy test; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Corrected QT interval (QTc) =\< 480 msec per Fridericia's formula AND PR interval =\< 200 msec (using 12-lead electrocardiography \[EKG\]) * Agreement by woman of childbearing potential and sexually active males to use an effective method of contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for three months following duration of study participation * A woman of childbearing potential is defined as a sexually mature woman who: * Has not undergone a hysterectomy or bilateral oophorectomy; or * Has not been naturally postmenopausal for at least 24 consecutive months FOR PATIENTS WITH MM OR CLL: \- At least 2 weeks from prior therapy to time of start of treatment; prior therapy includes steroids (except for =\< 10 mg daily prednisone or equivalent which is permitted during the study) Exclusion Criteria: * Current or planned use of other investigational agents, or concurrent biological, chemotherapy, or radiation therapy during the study treatment period * Use of a protease inhibitor for any indication within three months prior to start of study treatment * Current or planned use of prohibited meds * Liver disease, except Gilbert's syndrome, liver involvement by CLL or MM, or stable chronic liver disease per investigator's assessment * Current pancreatitis * History of allergic reactions or hypersensitivity attributed to compounds of similar chemical or biologic composition to metformin, ritonavir or any of their ingredients * Non-hematologic malignancy within the past 3 years aside from the following exceptions: * Adequately treated basal cell or squamous cell skin cancer * Carcinoma in situ of the cervix * Prostate cancer \< Gleason grade 6 with a stable prostate-specific antigen test (PSA) * Successfully treated in situ carcinoma of the breast * Clinically significant cardiac disease, including: * \>= Grade 2 myocardial infarction within 6 months prior to day 1 of protocol therapy * Unstable or uncontrolled disease condition relating to or affecting cardiac function (e.g. unstable angina, congestive heart failure, New York Heart Association Class III-IV) within 6 months prior to day 1 of protocol therapy * \>= Grade 2 uncontrolled cardiac arrhythmia * Clinically significant medical disease or condition that, in the investigator's opinion, may interfere with protocol adherence or the patient's ability to give informed consent * Women who are currently or planning to breastfeed during protocol treatment * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns or compliance with clinical study procedures, e.g., infection/inflammation, intestinal obstruction, unable to swallow medication, social/ psychological issues, uncontrolled intercurrent illness etc. * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)