A Study of Mirdametinib in Combination With Palbociclib in People With Liposarcoma

Inclusion Criteria: Phase I only: * A diagnosis of unresectable, recurrent, or metastatic DDLPS * Measurable disease as defined by RECIST 1.1 Phase II only: * A diagnosis of unresectable, recurrent (e.g. recurrent retroperitoneal) or metastatic DDLPS * Any number of prior lines of therapy * Measurable disease and evidence of progression of disease as defined by RECIST 1.1 (including newly diagnosed disease, new disease sites in a patient who was previously NED, or a 20% growth of existing lesions within 6 months of registration) * Age ≥ 18 years * ECOG performance status ≤ 2 * Adequate organ and marrow function as defined below (ULN indicates institutional upper limit of normal): * Absolute neutrophil count ≥ 1.5 x 109/L * Hemoglobin ≥ 9.0 g/dL * Platelets ≥ 100 x 109/L * Total bilirubin ≤ 1.5 X ULN OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 ULN, except patients with Gilbert's disease (≤3x ULN) * AST (SGOT) /ALT (SGPT) ≤ 1.5 x institutional ULN * Creatinine Clearance ≥ 60 mL/min (calculated by Cockcroft-Gault method) * Adequate coagulation function, as determined by: * International Normalized Ratio (INR) ≤ 1.5 × ULN (Grade ≤ 1). If the participant receives anticoagulant therapy, the INR \> 1.5 × ULN is permitted but the dose must be stable for at least 2 weeks before the start of the study treatments. * PTT ≤ 1.5 × ULN. * Adequate cardiac function, as determined by: * Systolic blood pressure \< 160 mmHg and diastolic blood pr…