Poly ICLC, Radiation, and Romidepsin for Advanced Cutaneous T Cell Lymphoma

Inclusion Criteria: * Must have prior biopsy at any time point diagnostic for confirmed MF stage IIA-IVA, and must have failed at least one standard therapy (topical or systemic). * Must have a skin lesion of at minimum 2 cm, in a location amenable to radiation and a minimum of 2 additional measurable skin lesions distant from the radiation site. * Must be either initiating therapy with romidepsin (Arm A) or currently receiving romidepsin with documented stable disease (SD) or partial response (PR) (Arm B). * Patient may have had any prior topical or systemic therapy except for total electron beam irradiation. Patients must be a minimum of 2 weeks from topical therapy and 4 weeks from systemic therapies, phototherapy, or local radiation therapy before enrollment except for HDACI if they are in Arm B. Patients are allowed to take weak potency topical corticosteroids if patient has been on a stable dose for more than a month. * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>70%) * Life expectancy of greater than 6 months * Patients must have normal organ and marrow function as defined below: * leukocytes \>=2,500/mcL * absolute neutrophil count \>=1,000/mcL * platelets \>=50,000/mcL * total bilirubin: within normal institutional limits * AST(SGOT, aspartate aminotransferase)/ALT(SGPT, alanine aminotransferase) =\<2.5 X institutional upper limit of normal * creatinine: within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal. * Age \>=18 years * The effects of focal radiation and HDACI on the developing human fetus are unknown. For this reason and because agents as well as other therapeutic agents used in this trial are known to be tetragenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks, or topical therapy within 2 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. Patients are allowed to take weak potency topical corticosteroids if patient has been on a stable dose for more than a month. * Patients who are receiving any other investigational agents. * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to HDACI, TLR-agonist, or patients with known history of pre-existing auto-immune disease. * Concurrent therapy with systemic corticosteroids or other immunosuppressive medications. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study HDACI is a class agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with HDACI, breastfeeding should be discontinued if the mother is treated with HDACI and radiation. Woman of childbearing age and men sexually active with woman of childbearing age must agree to an acceptable method of birth control (double barrier) while on study. * Patients with known HIV infection are ineligible because this immunomodulatory therapy requires a normal and functional T cell repertoire. If this study is found to be safe, effective, and immunogenic, HIV positive patients may be included in future studies.