Testing the Addition of Cemiplimab to Palbociclib for the Treatment of Advanced Dedifferentiated Liposarcoma

Inclusion Criteria: * ELIGIBILITY CRITERIA (STEP 1): Patients must have histologically documented dedifferentiated liposarcoma (DDLPS). Patients with mixed well-differentiated/dedifferentiated liposarcoma (WD/DD LPS) tumors are eligible provided there is a histologically confirmed DDLPS component at some point during the treatment course * Disease must be metastatic or locally advanced and surgically unresectable, in the opinion of the treating investigator * Note: Intact retinoblastoma protein (RB) can be assumed in DDLPS. In a query of project Genomics Evidence Neoplasia Information Exchange (GENIE) (American Association for Cancer Research \[AACR\]), including 286 DDLPS tumors, the rate of RB1 mutation in DDLPS was 1.37%. Therefore, molecular testing to determine intact Rb is not required * ELIGIBILITY CRITERIA (STEP 1): Patients must have at least one lesion that is measurable per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 criteria to be eligible for this study. Previously radiated lesions should not be used as target lesions unless there is documented evidence of disease progression of that lesion after radiation * ELIGIBILITY CRITERIA (STEP 1): Patients may have received any number of prior systemic treatment lines for DDLPS, including none * ELIGIBILITY CRITERIA (STEP 1): Patients must have recovered to baseline or =\< grade 1 per CTCAE version 5.0 from toxicity related to any prior treatment, unless adverse events are clinically nonsignifi…