Inclusion Criteria:

- Patients must have histological confirmation of a cutaneous T-cell lymphoma (CTCL) of
any histology; confirmation of histological diagnosis must be completed prior to
enrollment by the lead site (Northwestern)

- Patients will be stratified by mycosis fungoides (MF) and Sezary syndrome (SS)
(report diagnostic or consistent with MF/SS), stage IA-IVB according to TNM
blood (TNMB) classification versus other CTCL histologies

- Patients must have measurable disease (using modified Severity-Weighted Assessment
Tool [mSWAT]) and/or use of indicator lesions must be designated prior to study
enrollment (from imaging); measurable disease upon physical exam with a negative scan
is acceptable

- Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status
of =< 2

- Patients must have a life expectancy of >= 3 months

- Patients with MF/SS must have failed at least 1 prior topical therapy (including
steroids, nitrogen mustard, retinoids, phototherapy, photochemotherapy, radiation,
and total skin electron beam); there is no upper limit for prior therapies

- Serum creatinine =< 2.0 mg/dL

- Total bilirubin =< 2.2 mg/dL

- Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase [SGPT]) =< 2 x
upper limit of normal (ULN)

- Leukocytes >= 3,000/mm^3

- Absolute neutrophils >= 1,500/mm^3

- Platelets >= 100,000/mm^3

- Patients must have an electrocardiogram (EKG) demonstrating QTc =< 500 ms within 28
days prior to registration

- Females of child-bearing potential and sexually active males must agree to use
effective methods of contraception:

- Child-bearing potential is defined as any woman (regardless of sexual
orientation, having undergone a tubal ligation, or remaining celibate by choice)
who meets the following criteria:

- Has NOT undergone a hysterectomy or bilateral oophorectomy; OR

- Has NOT been naturally menopausal for at least 12 consecutive months (i.e.
has had menses at any time in the preceding 12 consecutive months)

- The effectiveness of hormonal contraceptives may be reduced by romidepsin, thus
effective methods should include at least 1 form of barrier contraception

- Females of child-bearing potential must have a negative pregnancy test within 7 days
prior to registration

- Patients must be disease free of any prior malignancies for >= 3 years

- The exception to this would be currently treated squamous cell and basal cell
carcinoma of the skin, carcinoma in situ of the cervix, breast, or bladder, or
surgically removed melanoma in situ of the skin (stage 0) with histologically
confirmed free margins of excision

- Patients must give written informed consent prior to registration on the study

Exclusion Criteria:

- Patients who have received topical therapy, systemic chemotherapy, or biological
therapy within 4 weeks prior to registration are NOT eligible for participation

- Patients who have undergone major surgery within 21 days prior to registration are
NOT eligible for participation

- Patients who have an acute active infection requiring treatment (systemic
antibiotics, antivirals, or antifungals) within 14 days prior to registration are NOT
eligible for participation

- Patients in whom IV fluid hydration is contraindicated (e.g. due to pre-existing
pulmonary, cardiac, or renal impairment) will NOT be eligible for participation

- Patients who are pregnant and/or lactating are NOT eligible for participation

- Patients who have had a prior stem cell transplantation are NOT eligible for
participation

- Patients who have had any of the following cardiac conditions are NOT eligible for
participation (unless otherwise noted):

- Unstable angina or myocardial infarction within 4 months prior to registration

- New York Heart Association (NYHA) class II or IV heart failure

- Uncontrolled angina

- A history of severe coronary artery disease

- Severe, uncontrolled ventricular arrhythmias

- Sick sinus syndrome

- Electrocardiographic evidence of acute ischemia or Grade 3 conduction system
abnormalities UNLESS the patient has a pacemaker

- Patients who exhibit uncontrolled hypertension (>= 140/90 mmHg) or uncontrolled
diabetes within 14 days prior to registration are NOT eligible for participation

- Patients who have experienced significant neuropathy (grades 3-4 or grade 2 with
pain) within 14 days prior to registration are NOT eligible for participation

- Patients who have a known history of allergy to Captisol (a cyclodextrin derivative
used to stabilize carfilzomib) are NOT eligible for participation

- Patients who have a 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) are NOT eligible for participation

- Patients with pleural effusions requiring thoracentesis or ascites requiring
paracentesis within 14 days prior to registration are NOT eligible for participation

- Patients who have any serious condition, laboratory abnormality, or psychiatric
illness that would prevent them from singing the informed consent form are NOT
eligible for participation

- Patients who have had prior exposure to romidepsin or any proteasome inhibitor are
NOT eligible for participation

- Patients with a known human immunodeficiency virus (HIV) infection are NOT eligible
for participation

- Patients who test positive for infectious hepatitis types A, B, or C within 14 days
of registration are NOT eligible for participation