A Phase II Study of Carfilzomib in the Treatment of Relapsed/Refractory Mantle Cell Lymphoma

Study Drug Administration: If participant is found to be eligible for this study, they will begin the first cycle of treatment with carfilzomib. Each cycle is 28 days. On Days 1, 2, 8, 9, 15, and 16 of Cycles 1-12: * Participant will receive carfilzomib by vein over 30 minutes. The first 2 doses participant receives may be lower than later doses. This is to reduce the risk of an allergic reaction. On Days 1, 2, 15, and 16 of Cycles 13 and beyond: * Participant will receive carfilzomib by vein over 30 minutes. Participant should drink at least 6-8 cups (8 ounces each) of fluid per day starting 2 days before their first day of treatment and for as long as their doctor asks them to. During Cycles 1 and 2, participant will receive fluids by vein before and after their dose of carfilzomib. Before participant receives carfilzomib, they will be given standard drugs (such as allopurinol, dexamethasone, antibiotics, anti-fungals, and/or anti-virals) to help decrease the risk of side effects. Participant may ask the study staff for information about how the drugs are given and their risks. When participant receives the drugs during Cycle 1 and on Day 1 of Cycle 2, they will be monitored for side effects for 1 hour after they receive the study drug. Study Visits: On Day 1 of all cycles: * Participant will have a physical exam. * Participant will have a neurological exam to check for weakness, numbness and pain in their hands and feet. * Blood (about 2 tablespoons) will be drawn for routine tests. * If participant's doctor thinks it is needed, they will have a bone marrow biopsy and/or aspiration to check the status of the disease. * If participant's doctor thinks it is needed, they will have an ECHO or a MUGA. * If participant is able to become pregnant, they will have a blood (about 1½ tablespoons) or urine pregnancy test. (Cycles 2 and beyond only) On Days 2, 9, and 16 of all cycles: * Participant's vital signs will be measured. On Days 8 and 15 of all cycles: * Participant will have a physical exam. * Blood (about 2 tablespoons) will be drawn for routine tests. * If participant is able to become pregnant, they will have a blood (about 1½ tablespoons) or urine pregnancy test. On Day 1 of Cycles 2, 4, 6, and so on up to Cycle 12, then every 3 cycles after that: * If the study doctor thinks it is needed, participant will have a CT scan, MRI, PET scan, and/or PET/CT scan to check the status of the disease. * If the study doctor thinks it is needed, participant will have a gastrointestinal endoscopy or colonoscopy. Length of Study: Participant may continue taking the study drug for up to 3 years. Participant will no longer be able to take the drug if the disease gets worse, if intolerable side effects occur, or if they are unable to follow study directions. Patient's participation on the study will be over once they have completed the long term follow-up phone calls. End-of-Treatment Visit: Within about 30 days, after participant finishes taking the study drug they will return to the clinic for the following tests and procedures: * Participant will have a physical exam. * Participant will have a neurological exam to check for weakness, numbness and pain in their hands and feet. * Participant will have an EKG to check their heart function. * Blood (about 3-5 tablespoons) will be drawn for routine tests and to check the status of the disease. * Participant will have a CT scan and/or x-ray to check the status of the disease. * Participant will have a PET/CT scan to check the status of the disease. * If participant's doctor thinks it is needed, they will have a bone marrow biopsy and aspiration * If participant's doctor thinks it is needed, they will have a colonoscopy/gastrointestinal endoscopy. * If participant is able to become pregnant, they will have a blood (about 1½ tablespoons) or urine pregnancy test. Long Term Follow-Up: After participant's end-of-treatment visit, they will be called every 6 months for 1 year to see how they are doing and to find out about any other treatments they have received since they stopped study treatment. These calls will take about 2-3 minutes. In addition to the phone calls, participant's medical records may be reviewed as well. This is an investigational study. Carfilzomib is FDA approved and commercially available for the treatment of certain types of multiple myeloma. This drug is investigational for the treatment of MCL. Up to 60 participants will be enrolled on this study. All will be enrolled at MD Anderson.