Carfilzomib in Treating Patients With Relapsed or Refractory T-Cell Lymphoma

Inclusion Criteria:

* Relapsed and refractory PTCL, including angioimmunoblastic T-cell lymphoma (AITL), anaplastic large cell lymphoma (ALCL) ALK+/ALK-, adult T-cell leukemia/lymphoma (ATLL), NK-cell lymphoma (NKL), transformed MF to large cell, and PTCL-unspecified (PTCL-U) patients who have failed standard therapy/transplant for their histological confirmed disease or who are not transplant eligible are eligible to participate in this trial
* Karnofsky performance status \>= 70
* ANC \>= 700 cells/mm\^3, unless due to lymphoma involvement of the bone marrow or spleen
* Platelet count \>= 50 mm\^3, unless due to lymphoma involvement of the bone marrow or spleen
* Hemoglobin \>= 8 g/dL, unless due to lymphoma involvement of the bone marrow
* Liver functions (AST, ALT, bilirubin) =\< 3 x upper limits of normal (ULN) unless due to lymphoma or due to Gilberts disease
* Serum creatinine \< 2.0 mg/dL or calculated creatinine clearance (CrCl) \> 40 mL/min (Cockcroft-Gault)
* LVEF \>= 40% 2-D transthoracic ECHO is the preferred method of evaluation; MUGA scan is acceptable if ECHO is not available
* Able to adhere to the study visit schedule and other protocol requirements
* Patients must be willing to give written informed consent, and sign an institutionally approved consent form before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care
* Non-pregnant and non-nursing; men and women of reproductive potential may not participate unless they have agreed to use an effective contraceptive method while on the study
* No serious disease or condition that, in the opinion of the investigator, would compromise the patient's ability to participate in the study
* Patients with a history of coronary artery disease, congestive heart failure, hypertension, diabetes, or hyperlipidemia must have a MUGA or echocardiography, performed within 2 months of study entry

Exclusion Criteria:

* Pregnant or breast feeding females
* Active serious infection requiring treatment within 14 days prior to the start of carfilzomib
* Active hepatitis or uncontrolled HIV
* Unstable angina or myocardial infarction within 6 months prior to enrollment, 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 EKG 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 start of carfilzomib
* Patients in whom the schedule of oral and IV fluid hydration is contraindicated, e.g., due to pre-existing pulmonary, cardiac, or renal impairment
* Prior malignancies within the past 2 years with exception of adequately treated basal cell, squamous cell skin cancer, or thyroid cancer; carcinoma in situ of the cervix or breast; prostate cancer of Gleason grade 6 or less with stable prostate specific antigen (PSA) levels
* Significant peripheral neuropathy (grades 3-4, or grade 2 with pain) within 14 days prior to the start of carfilzomib
* Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib)
* Concurrent use of other anti-cancer agents, investigative agents, or treatments
* Contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to all anticoagulation and antiplatelet options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment
* Any other clinically significant medical disease or condition laboratory abnormality or psychiatric illness that, in the Investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent