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