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 aminotra…