Carfilzomib, Bendamustine Hydrochloride, and Dexamethasone in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Relapsed and or refractory multiple myeloma after at least one prior line of therapy; there is no upper limit of prior lines of therapy; patients who are ineligible for stem cell transplantation are allowed; patients should have received at least one prior novel agent (immunomodulatory agents or proteasome inhibitors); patients eligible for bone marrow transplant must have undergone bone marrow transplant (BMT) prior to enrollment * Measurable disease, as defined by one or all of the following (assessed within 30 days prior to initiation of therapy): a) serum M-protein \>= 0.5 g/d; b) urine Bence-Jones protein \>= 200 mg/24 hours; c) patients with light chain only myeloma are eligible; the involved free light chain level 100 mg/L with abnormal serum free light chain ratio * Documented relapse or progressive disease on or after any regimen (subjects refractory to the most recent regimen are eligible) * Primary refractory patients (never responded to any therapy) are eligible * Eastern Cooperative Oncology Group performance status 0 - 2 * Serum alanine aminotransferase (ALT) \< 3.5 times the upper limit of normal within 30 days prior to cycle 1 day 1 * Serum direct bilirubin \< 2 mg/dL (34 Omol/L) within 30 days prior to cycle 1 day 1 * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L within 30 days prior to cycle 1 day 1, without granulocyte-colony stimulating factor (G-CSF) * Hemoglobin \> 9 g/dL (80 g/L) within 30 days prior to cycle 1 day 1 (subjects may be receiving red blood cell transfusions in accordance with institutional guidelines) * Platelet count \> 100 x 10\^9/L (30 x 10\^9/L if myeloma involvement in the bone marrow aspirate is \> 50%) within 30 days prior to cycle 1 day 1; subjects may receive platelet transfusions within institutional guidelines * Creatinine clearance \> 50 mL/minute within 30 days prior to cycle 1 day 1, either measured or calculated using a standard formula * Patient should have a normalized or normal uric acid level prior to study entry * Written informed consent in accordance with federal, local, and institutional guidelines * Females of childbearing potential must have a negative pregnancy test and agree to ongoing pregnancy testing and to practice contraception; (birth control methods should be determined in consultation with the investigator) * Male subjects must agree to practice contraception Exclusion Criteria: * Intolerance to previous bendamustine, carfilzomib or dexamethasone or mannitol; subjects who are allergic to bortezomib are not excluded * Chemotherapy (approved or investigational) within 3 weeks prior to the first day of treatment or antibody therapy within 6 weeks prior to the first day of treatment * Radiotherapy to \>= 3 sites at the same time within 1 week prior to the first day of treatment * Immunomodulatory therapy such as immunomodulatory drugs (Imids) or stem cell transplant within 28 days prior to the first day of treatment * Pregnant or lactating females * Major surgery within 21 days prior to the first day of treatment * Acute active infection requiring treatment (IV antibiotics, antivirals, or antifungals) within 14 days prior to the first day of treatment * Known human immunodeficiency virus infection * Known active hepatitis B or C infection * Unstable angina or myocardial infarction within 4 months prior to the first day of treatment, the New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, history of severe coronary artery disease, severe uncontrolled ventricular arrhythmias, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or grade 3 conduction system abnormalities unless subject has a pacemaker * Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to the first day of treatment * Non-hematologic malignancy within the past 3 years with the exception of a) adequately treated basal cell carcinoma, squamous cell skin cancer, or thyroid cancer; b) carcinoma in situ of the cervix or breast; c) prostate cancer of Gleason grade 6 or less with stable prostate-specific antigen levels; or d) cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study, such as localized transitional cell carcinoma of the bladder or benign tumors of the adrenal or pancreas * Significant neuropathy (grades 3 - 4, or grade 2 with pain) within 14 days prior to the first day of treatment * Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) * Contraindication to any of the required concomitant drugs or supportive treatments or intolerance to hydration due to preexisting pulmonary or cardiac impairment * Subjects with known or likely systemic amyloidosis * Ongoing graft-vs-host disease * Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days prior to the first day of treatment * Any other clinically significant medical disease or condition that, in the investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent