Bortezomib and Azacitidine in Treating Patients With Relapsed or Refractory T-Cell Lymphoma

Inclusion Criteria: * Patients must have pathologically documented T-cell lymphoma belonging to one of the following WHO entities: Peripheral T-cell lymphoma, not otherwise specified (PTCL-NOS); Mycosis Fungoides and Sezary Syndrome (MF-SS); Angioimmunoblastic T-cell lymphoma (AITL); CD30-positive Anaplastic Large Cell Lymphoma (ALCL), systemic; T/NK-cell lymphoma, extranodal, nasal and nasal type; Hepatosplenic T-cell lymphoma, gamma/delta or alpha/beta; Enteropathy-associated T-cell lymphoma (EATL); Adult T-cell Leukemia/Lymphoma (ATLL); Subcutaneous panniculitis-like T-cell lymphoma (SCPTCL); Blastic T/NK-cell lymphoma/leukemia (CD4+CD56+ Hematodermic Tumor); T/NK-cell post-transplant lymphoproliferative disorders (PTLD); Large Granular Lymphocyte (LGL) Leukemia; T-cell Prolymphocytic Leukemia (T-PLL) * Patients must have relapsed or refractory TCL * Patients must have failed at least one prior systemic therapy * Life expectancy must be greater than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Patients must have adequate organ function as defined below: * Total bilirubin \< 1.5 x upper limit of normal (ULN) * AST(aspartate aminotransferase) \< 2.0 x ULN * ALT(Alanine transaminase) \< 2.0 x ULN * Serum creatinine \< 1.5 ULN * New York Heart Association Congestive Heart Failure (NYHA CHF) Class II or better * Platelet count \>= 75,000/mm\^3 (unless due to disease) within 14 days before enrollment * Absolute neutrophil count of \>= 1,500/mm\^3 within 14 days before enrollment * Women of childbearing potential must have a negative serum pregnancy test prior to azacitidine treatment; 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; if the patient does not agree, the patient is not eligible; women must agree to not get pregnant for the duration of the study; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform the PI or the Study Nurse immediately * Ability to understand and willingness to sign the written informed consent document 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performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * Male subject agrees to use an acceptable method for contraception for the duration of the study Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study * Patients receiving any other investigational agents or patients who have received other investigational agents within 14 days of enrollment * Patients with active central nervous system (CNS) malignancy * Patients with history of allergic reactions attributed to compounds of similar chemical or biologic composition to Azacitidine or VELCADE (BORTEZOMIB) that are not easily managed; patients with hypersensitivity to VELCADE (BORTEZOMIB), boron, or mannitol * Patients must not have previously received Azacitidine or VELCADE (BORTEZOMIB) for any disease * Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, serious cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; as infection is a common feature of TCL, patients with active infection are permitted to enroll provided that the infection is under control; myocardial infarction within 6 months prior to enrollment or has NYHA Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities; prior to study entry, any ECG abnormality at screening has to be documented by the investigator as not medically relevant * Pregnant women or women who are breastfeeding are excluded from this study; confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (beta-hCG) pregnancy test result obtained during screening; pregnancy testing is not required for post-menopausal or surgically sterilized women * HIV-positive patients are ineligible; all patients will be screened for HIV * Patients with pre-existing Grade 2 or higher neuropathy within 14 days before enrollment or other serious neurologic toxicity that would significantly increase risk of complications from VELCADE (BORTEZOMIB) therapy are excluded * Patients with active, advanced malignant solid tumors are excluded * Patients with serious medical or psychiatric illness likely to interfere with participation in this clinical study * Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy