A Phase II Study Evaluating the Efficacy of Ruxolitinib in Patients With T-Cell Large Granular Lymphocytic Leukemia (T-LGLL)

Inclusion Criteria: * Age 18 or older and able to swallow pills * Diagnosis of T-LGLL defined as: LGL cell population meeting diagnostic criteria (defined as CD3+CD8+ cell population \>650/mm3 or CD3+CD8+CD57+ population \>500/mm3 or LGL cell population with other immunophenotype that includes co-expression of CD3+, CD8+, CD57+ with \>500 cells/mm3 and the presence of a clonal T-cell receptor (within 1 month of diagnosis or relapse). This also includes patients with rare T-LGLL variants include CD4+ T-LGLL, and gamma/delta T-LGLL which can be CD4- and CD8-), though patients still must have the presence of a clonal T-cell receptor within 1 month of diagnosis or relapse. Note: patients with MDS-like T-LGLL may be included with PI approval even if CD3+CD8+ cell population is \< 650/mm\^3, though +TCR is required. Natural-Killer (NK) LGL is also permitted, provided there is a clonal NK-cell population noted with \> 500 cells/mm\^3 * Untreated T-LGLL or failed at least one line of frontline therapy; * Patients must be 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. Platelet transfusion may be utilized to meet inclusion criteria, as long as the platelet count remains \>50,000/uL within 5 days of last transfusion. Note: Patients with platelets \<100 x 109/L and renal impairment are not permitted to enroll to the study. Renal impairment is defined as creatinine clearance (CrCl) \< 90 mL/min. * Serum creatinine =\< 2 x the upper limit of normal (ULN) * \- Estimated glomerular filtration rate (eGFR) =\> 30 mL/min using the Modification of Diet in Renal Disease (MDRD) equation (multiplying eGFR by each subjects Body Surface Area \[BSA\]) * 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) =\< 2.5 x ULN * Alkaline phosphatase (ALP) =\< 2.5 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 treatment until 5 half-lives have passed. Male subject agrees to use an acceptable method for contraception for the duration of the study treatment until 5 half-lives have passed. * Able to sign informed consent Exclusion Criteria: * Absolute neutrophil count (ANC) less than 100/mm\^3. Note: granulocyte colony-stimulating factor (G-CSF) may be utilized to enable patients to meet inclusion criteria, as long as the ANC remains above 100/mm\^3 for 5 days after administration of last growth-factor. * 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. Patients with tuberculosis risk factors will be required to undergo quantiferon testing and/or purified protein derivative (PPD) testing with a negative result prior to entering the study. * Concurrent immune-suppressive therapy (prednisone or equivalent up to 20 mg permitted to treat LGLL 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 principal investigator (PI). Early stage skin cancers, prostate cancer, permitted if under no active therapy * For females of childbearing potential: Positive pregnancy test or lactating * Unstable angina or myocardial infarction within the past 2 months * Chronic obstructive pulmonary disease or other interstitial lung disease in active exacerbation * Cirrhosis * For any strong CYP3A4 inhibitors deemed a moderate or severe risk of interaction with ruxolitinib, a wash-out period of 14 days, or 5 half-lives, whichever is longer, is needed prior to starting ruxolitinib * Given the CYP3A4 inhibition potential of grapefruit, grapefruit juice, Seville orange juice, pomelos, and starfruits, patients will need to refrain from these foods/drinks for 14 days prior to initiation of therapy, and throughout the study period