Dose-Escalation Trial of Carfilzomib With and Without Romidepsin in Cutaneous T-Cell Lymphoma

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