Itacitinib in Treating Patients With Refractory Metastatic/Advanced Sarcomas

Inclusion Criteria: * Subjects \>= 18 years old * Must have a histologically confirmed diagnosis of sarcoma with one of the following subtypes: * Cohort 1: Leiomyosarcoma * Cohort 2: Undifferentiated pleiomorphic sarcoma * Cohort 3: Synovial sarcoma or myxoid/round cell liposarcoma * Cohort 4: Chondrosarcoma (all subtypes of chondrosarcoma are allowed) * Subjects enrolling to cohorts 1, 2, or 3 must have received at least two prior lines of systemic therapy. Subjects enrolling to cohort 4 only may have received any number of prior lines of systemic therapy or may be treatment naïve * All ongoing toxicities related to prior therapies must be resolved to grade 1 or better (except alopecia) * Subjects must have one or more measurable lesions, as determined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 assessed by computed tomography (CT) or magnetic resonance imaging (MRI) * Subjects must have at least one superficial lesion accessible for multiple biopsies; the tumor being biopsied cannot have been previously targeted for radiation therapy or have previously received intra-lesional treatment \* NOTE: Superficial lesions previously targeted with radiation therapy that have demonstrated significant new growth via radiological imaging may be targeted for biopsy, with sponsor-investigator approval. * Total bilirubin level =\< 1.5 x the upper limit of normal (ULN) range mg/dL * Aspartate aminotransferase (AST) =\< 2.5 x ULN and alanine aminotransferase (ALT) levels =\< 2.5 x ULN * Alkaline phosphatase \< 2.5 x ULN * Serum creatinine =\< 1.5 x ULN * Calculated creatinine clearance \>= 30 mL/min using the Cockcroft-Gault formula may be included * Absolute neutrophil count (ANC) \>= 1.5 × 10\^9/L * Platelet count \>= 100 x 10\^9/L; transfusion is permitted as clinically indicated * Hemoglobin \>= 9 g/dL \* Transfusion is permitted as clinically indicated * Subjects must have a life expectancy \>= 6 months, as determined by the treating physician * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 or Karnofksy performance status \>= 60 * Male or non-pregnant and non-breast feeding female: * Females of child-bearing potential must agree to use highly effective contraception without interruption from initiation of therapy and while on study medication and have a negative serum pregnancy test (beta - human chorionic gonadotropin \[hCG\]) result at screening and agree to ongoing pregnancy testing during the course of the study, and at the end of study treatment; a highly effective method of contraception is defined as one that results in a low failure rate (that is, \< 1% per year), when used consistently and correctly, such as implants, injectables, combined oral contraceptives, some intrauterine contraceptive devices, sexual abstinence, or a vasectomized partner * Male subjects must practice abstinence or agree to use a condom during sexual contact with a pregnant female or a female of childbearing potential while participating in the study * Ability to understand and sign informed consent document * Willingness and ability to comply with scheduled visits, laboratory tests, and other study procedures Exclusion Criteria: * Known active, uncontrolled, or symptomatic central nervous system (CNS) metastases; a subject with controlled and asymptomatic CNS metastases may participate in this study; as such, the subject must have completed any prior treatment for CNS metastases \>= 28 days (including radiotherapy and/or surgery) prior to the start of treatment in this study and should not be receiving chronic corticosteroid therapy for CNS metastases; subjects with known CNS metastases must be confirmed radiographically stable by at least one imaging study, at least 28 days from last treatment * Receipt of any type of cytotoxic, biologic, or other systemic anticancer therapy (including investigational) within 2 weeks of enrollment * Prior treatment with a drug targeting JAK1, JAK1/2 or STAT3 inhibitor; Food and Drug Administration (FDA) approved small molecule tyrosine kinase inhibitors (TKIs) not specifically designed to target this pathway are okay (e.g. pazopanib, sunitinib, sorafenib) * Known, active drug or alcohol abuse * Pregnant or lactating females * Active or recent infection requiring systemic anti-infective treatment that was completed =\< 14 days prior to enrollment (with the exception of uncomplicated urinary tract infection or upper respiratory infection) * Uncontrolled or concurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Oral steroid usage within =\< 14 days prior to enrollment * Known inflammatory or autoimmune disease which requires patient to occasionally require high dose oral steroids * Subjects with known, active human immunodeficiency virus (HIV) infection (subjects with undetectable viral load and normal CD4+ T-cell count are permitted) * Inability to swallow food or tablets, or significant gastrointestinal disorder that, in the opinion of the investigator, could interfere with absorption of the study drug * Previous reaction to any component of itacitinib or known hypersensitivity to the active substance or any of the excipients * Subjects with a sarcoma which has other, defined treatments or biology distinctly different from those of soft tissue sarcomas in general; including, but not limited to, Ewing's sarcoma, rhabdomyosarcoma, gastrointestinal stromal tumors, Kaposi's sarcoma, Wilm's tumor