Inclusion Criteria:  Age 18 or older Diagnosis of T-LGLL defined as: CD3+CD8+ cell population > 650/mm^3 and the presence of a clonal T-cell receptor (within 1 month of diagnosis). Note: patients with myelodysplastic syndrome (MDS)-like T-LGLL may be included with principal investigator (PI) approval even if CD3+CD8+ cell population is < 650/mm^3, though +TCR is required. Natural-killer (NK) large granular lymphocytic leukemia (LGL) is also permitted, provided there is a clonal NK-cell population noted with > 500 cells/mm^3 Failed at least one line of frontline therapy; off treatment for at least 14 days or 5 half-lives, whichever is longer  Require Treatment for T-LGLL (One or more required)  Symptomatic anemia with hemoglobin < 10 g/dL Transfusion-dependent anemia Neutropenia with absolute neutrophil count (ANC) < 500/mm^3 Neutropenia with ANC < 1500/mm^3 with recurrent infections Platelet count >= 50 x 10^9/L Serum creatinine =< 2 x the upper limit of normal (ULN) Total bilirubin =< 1.5 x ULN (patients with Gilbert's syndrome with a bilirubin > 1.5 x ULN permitted) Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 1.5 x ULN Eastern cooperative oncology group (ECOG) performance status =< 2 Men and women of reproductive potential must agree to follow accepted birth control methods for the duration of the study. Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study. Male subject agrees to use an acceptable method for contraception for the duration of the study Able to sign informed consent  Exclusion Criteria:  Absolute neutrophil count (ANC) less than 200/m Active Infection requiring ongoing anti-microbial treatment. Patients with human immunodeficiency virus (HIV), positive hepatitis B surface antigen or hepatitis C antibody will be excluded Concurrent immune-suppressive therapy (prednisone or equivalent up to 20 mg permitted to treat T-LGL symptoms, but must be weaned within one month of initiation of trial drug). Patients on stable, chronic prednisone =< 10 mg for rheumatologic/autoimmune conditions are exempted from this requirement. They may enroll on the study Active, concurrent malignancy unless deemed related to T-LGLL by PI Prior use of 5-azacytidine or decitabine Positive pregnancy test