Efatutazone Dihydrochloride in Treating Patients With Previously Treated Myxoid Liposarcoma That Cannot Be Removed by Surgery

* Patients must have a formalin-fixed, paraffin-embedded (FFPE) tumor block OR 1 representative hematoxylin and eosin (H\&E) and 20 unstained myxoid liposarcoma tissue slides available for submission to central pathology review; this review is mandatory prior to registration to confirm eligibility
* Measurable disease
* Progression on at least one prior systemic chemotherapy for advanced, unresectable or metastatic disease; prior adjuvant or neoadjuvant therapy is not included as prior systemic chemotherapy unless treatment occurred within the 6 months prior to study enrollment

  * There is no limit to the number of prior lines of treatment a patient has received
  * No treatment with biologic therapy, immunotherapy, chemotherapy, investigational agent for malignancy, or radiation =\< 28 days before study registration; no treatment with nitrosourea or mitomycin =\< 42 days before study registration
  * Patients should have resolution of any toxic effects of prior therapy (except alopecia) to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version 4.0, grade 1 or less
* No history of the following:

  * Class III or IV congestive heart failure (CHF)
  * Pericardial effusion =\< 12 months (grade 3 or 4)
  * Pericardial involvement with tumor
  * Grade 2 or higher pleural effusion =\< 6 months
* No symptomatic, untreated, or uncontrolled brain metastases present
* Not pregnant and not nursing; for women of childbearing potential only, a negative pregnancy test done =\< 7 days prior to registration is required; a female of childbearing potential is a sexually mature female who:

  * Has not undergone a hysterectomy or bilateral oophorectomy; or
  * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months)
* Patients with diabetes mellitus requiring concurrent treatment with insulin or thiazolidinedione (TZD) oral agents are not eligible
* Patients with known hypersensitivity to any TZD oral agents are not eligible
* Eastern Cooperative Oncology Group (ECOG) performance status 0-2
* Absolute neutrophil count (ANC) \>= 1,000/mm\^3
* Platelet count \>= 75,000/mm\^3
* Creatinine =\< 1.5 mg/dL x upper limits of normal (ULN) OR calculated (calc.) creatinine clearance \>= 30 mL/min
* Bilirubin =\< 1.5 x ULN; for subjects with liver metastases =\< 3 x ULN is allowed
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 x ULN; for subjects with liver metastases, SGOT (AST) and SGPT (ALT) \< 5 x the upper normal limit of institution's normal range is allowed
* Eligible patients must have histopathologically confirmed myxoid liposarcoma with confirmation of DDIT3 rearrangement