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 may not have received prior treatment with CDK4/6 inhibitors (including, but not limited to: palbociclib, ribociclib or abemaciclib) or anti-PD-1/anti-PD-L1 antibodies
* 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 nonsignificant and/or stable on supportive therapy, and with the exceptions of fatigue (which must be =\< grade 2), alopecia and/or endocrinopathies related to prior immunotherapy which are controlled with hormone replacement
* ELIGIBILITY CRITERIA (STEP 1): Patients must have completed all prior anti-cancer treatment, including radiation, \>= 14 days prior to registration
* ELIGIBILITY CRITERIA (STEP 1): Age \>= 18 years
* ELIGIBILITY CRITERIA (STEP 1): Eastern Cooperative Oncology Group (ECOG) Performance Status 0-2
* ELIGIBILITY CRITERIA (STEP 1): Absolute neutrophil count (ANC) \>= 1000/mm\^3
* ELIGIBILITY CRITERIA (STEP 1): Platelet count \>= 100,000/mm\^3
* ELIGIBILITY CRITERIA (STEP 1): Hemoglobin \>= 9 g/dL
* ELIGIBILITY CRITERIA (STEP 1): Creatinine clearance (CrCl) \>= 30 mL/min
* ELIGIBILITY CRITERIA (STEP 1): Total bilirubin =\< 1.5 x upper limit of normal (ULN)
* ELIGIBILITY CRITERIA (STEP 1): Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3.0 x ULN
* ELIGIBILITY CRITERIA (STEP 1): Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible, patients should be class IIB or better. Furthermore, patients may not have an uncontrolled ventricular arrhythmia or recent (within 3 months) myocardial infarction
* ELIGIBILITY CRITERIA (STEP 1): For patients with evidence of chronic hepatitis B (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
* ELIGIBILITY CRITERIA (STEP 1): Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently receiving treatment, they are eligible if they have an undetectable HCV viral load
* ELIGIBILITY CRITERIA (STEP 1): Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* ELIGIBILITY CRITERIA (STEP 1): Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. Patients participating on this trial may not be receiving other anti-neoplastic therapies and there should be no anticipated need for such therapy
* ELIGIBILITY CRITERIA (STEP 1): Patients with treated brain metastases that are non-progressing are eligible if follow-up brain imaging performed at least 4 weeks after central nervous system (CNS)-directed therapy shows no evidence of progression. Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are not eligible
* ELIGIBILITY CRITERIA (STEP 1): Patients must not have an uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on high resolution computed tomography (HRCT) scan or any other condition that would limit compliance with study requirements
* ELIGIBILITY CRITERIA (STEP 1): Patients must be able to swallow oral medications
* ELIGIBILITY CRITERIA (STEP 1): Patients may not require the use of chronic steroids in excess of 10 mg prednisone daily or equivalent
* ELIGIBILITY CRITERIA (STEP 1): Patients may not require concomitant use of known strong CYP3A inhibitors (e.g., itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir)
* ELIGIBILITY CRITERIA (STEP 1): Patients may not require concomitant use of known strong CYP3A inducers (e.g., phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort)
* RE-REGISTRATION ELIGIBILITY CRITERIA (FOR STEP 2 CROSSOVER FROM ARM 1 TO ARM 2): In order to cross over to Arm 2, patients must meet the same eligibility criteria as described above
* RE-REGISTRATION ELIGIBILITY CRITERIA (FOR STEP 2 CROSSOVER FROM ARM 1 TO ARM 2): Patients must have demonstrated progression of disease on palbociclib monotherapy (Arm 1) per RECIST version 1.1 criteria
* RE-REGISTRATION ELIGIBILITY CRITERIA (FOR STEP 2 CROSSOVER FROM ARM 1 TO ARM 2): Patients may not have experienced a grade 3 or higher non-hematologic adverse event deemed clinically significant in the opinion of the treating investigator, or have discontinued palbociclib due to toxicity, while participating on Arm 1

  * Patients must also have recovered to baseline or =\< grade 1 per CTCAE version 5.0 from toxicity related to Arm 1 treatment, unless adverse events are clinically nonsignificant and/or stable on supportive therapy, and with the exceptions of fatigue (which must be =\< grade 2), alopecia and/or endocrinopathies related to prior immunotherapy which are controlled with hormone replacement
  * Note: Patients who underwent dose reduction of palbociclib during treatment on Arm 1 will begin treatment on Arm 2 at the same dose (i.e. dose re-escalation is not allowed)
* RE-REGISTRATION ELIGIBILITY CRITERIA (FOR STEP 2 CROSSOVER FROM ARM 1 TO ARM 2): Patients may not have received prior treatment with anti-PD-1/anti-PD-L1 antibodies
* RE-REGISTRATION ELIGIBILITY CRITERIA (FOR STEP 2 CROSSOVER FROM ARM 1 TO ARM 2): Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects \* Therefore, for women of childbearing potential only, a negative serum pregnancy test done =\< 7 days prior to re-registration is required