Carfilzomib in Treating Patients With Chronic Graft-Versus-Host Disease

Inclusion Criteria: * Diagnosis of chronic GVHD according to National Institutes of Health (NIH) Consensus Criteria * May have either classic chronic GVHD or overlap subtype of chronic GVHD * Failure of at least one prior line of systemic immune suppressive therapy for management of chronic GVHD * Subject underwent transplantation at least 3 months prior to enrollment * Anticipated life expectancy \>= 6 months * Alanine aminotransferase (ALT) =\< 3.5 times the upper limit of normal, unless due to chronic GVHD * Bilirubin =\< 2 mg/dL, unless due to chronic GVHD * Absolute neutrophil count (ANC) \>= 1.0 × 10\^9/L * Hemoglobin \>= 8 g/dL * Platelet count \>= 50 × 10\^9/L * Creatinine clearance (CrCl) \>= 15 mL/minute, either measured or calculated * Signed informed consent in accordance with federal, local, and institutional guidelines * Females of childbearing potential (FCBP) must agree to a pregnancy test at study enrollment and to practice contraception during the study * Male subjects must agree to practice contraception during the study Exclusion Criteria: * Evidence of recurrent or progressive underlying malignant disease * Pregnant or lactating females * Surgery within 21 days prior to enrollment * Does not include placement of venous access device, bone marrow biopsy, GVHD diagnostic biopsy, or other routine procedures in chronic GVHD or post-transplantation care * Uncontrolled infection within 14 days prior to enrollment * Infection treated with appropriate antimicrobial therapy and without signs of progression/treatment failure does not constitute an exclusion criterion * Documented human immunodeficiency virus (HIV) infection * Active hepatitis B or C infection * Documented unstable angina or myocardial infarction within 6 months prior to enrollment, New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or grade 3 conduction system abnormalities (unless subject has a pacemaker), left ventricular ejection fraction (LVEF) \< 40%, history of torsade de pointe * Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to enrollment * Sustained systolic blood pressure \> 160 or diastolic blood pressure \> 100 despite medical therapy; sustained blood sugar \> 300 despite medical therapy * Chronic hypertension or diabetes on appropriate medical therapy does not constitute an exclusion criterion * Non-hematologic malignancy within the past 3 years with the exception of: * Adequately treated basal cell carcinoma, 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 levels * Cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study * Significant neuropathy per Common Terminology Criteria for Adverse Events (CTCAE) version (ver.) 4.03 or current version (grade 3 and above, or grade 2 with pain) within 14 days prior to enrollment * History of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) * Contraindication to all available herpes simplex virus (HSV)/varicella prophylactic antiviral drugs * Pleural effusions requiring thoracentesis, or ascites requiring paracentesis, within 14 days prior to enrollment * Any other clinically significant medical or psychological disease or condition that, in the investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent * New systemic immune suppressive agent added for the treatment of chronic GVHD within 2 weeks prior to enrollment * Treatment with a non-Food and Drug Administration (FDA) approved drug in the previous 4 weeks