Pembrolizumab and Radiation Therapy With or Without Neoadjuvant Doxorubicin and Ifosfamide for the Treatment of High-Risk Resectable Undifferentiated Pleomorphic Sarcoma or Liposarcoma of the Extremity or Trunk Wall

Inclusion Criteria: * Age ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2 * Histologically proven diagnosis of UPS or LPS originating in an extremity or trunk wall. Alternative terms for UPS include but are not limited to the following: * Fibrosarcoma * Malignant fibrous histiocytoma * Myxofibrosarcoma * Pleomorphic fibroblastic sarcoma * Pleomorphic sarcoma with giant cells * Pleomorphic sarcoma with prominent inflammation * Pleomorphic spindle cell sarcoma * Pleomorphic undifferentiated sarcoma * Spindle cell sarcoma, not otherwise specified (NOS) * Unclassified spindle cell sarcoma * Undifferentiated high-grade pleomorphic sarcoma * Please contact the medical monitor or study principal investigator (PI) with any questions regarding potentially eligible histologies * Tumor size ≥ 5 cm on anatomic imaging (computed tomography \[CT\] or magnetic resonance imaging \[MRI\]) * Fédération Nationale des Centres de Lutte Contre le Cancer (FNCLCC) grade (G)3 * Eligible for definitive local management of soft-tissue sarcoma (STS) per established guidelines with wide oncologic resection as determined by a surgeon with expertise in STS management * Must be a candidate for neoadjuvant radiation as part of local control plan as determined by a radiation oncologist with expertise in STS management * Hemoglobin ≥ 9.0 g/dL without transfusion within 7 days of enrollment * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L * Platelets ≥ 100 x 10\^9/L * Serum creatinine ≤ 1.5 x institutional upper limit of normal (ULN), or estimated glomerular filtration rate (eGFR) ≥ 60 ml/min/m\^2 (modification of diet in renal disease \[MDRD\] formula) for patients with serum creatinine \> 1.5 x institutional ULN * Bilirubin ≤ 1.5 x institutional ULN (in patients with a documented history of Gilbert's syndrome, bilirubin ≤ 3 x institutional ULN) * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase \[SGPT\]) ≤ 2.5 x institutional ULN * In patients for whom prothrombin time (PT) and international normalized ratio (INR) testing is clinically indicated, PT or INR must be ≤ 1.5 x ULN in patients not on anticoagulation. In patients receiving anticoagulant therapy, PT and INR must be within therapeutic range for the given anticoagulant * In patients for whom partial thromboplastin time (PTT) testing is clinically indicated, PTT must be ≤ 1.5 x ULN in patients not on anticoagulation. In patients receiving anticoagulant therapy, PTT must be within therapeutic range for the given anticoagulant * Clinically normal cardiac function based on left ventricular ejection fraction (LVEF) ≥ 50% * In patients for whom 12-lead electrocardiogram (ECG) is indicated, ECG without clinically significant abnormalities * Women of childbearing potential (WOCBP) must have a negative serum pregnancy test within 3 days prior to randomization * Subjects in both arms must agree to use highly effective birth control measures during the study treatment period and for at least 6 months after the last dose of chemotherapy or date of surgery, whichever is later * Female subjects who are breastfeeding should discontinue nursing prior to the first day of study treatment and abstain from nursing until 6 months after the last study treatment Exclusion Criteria: * Patients with evidence of nodal metastases or distant metastases (DM) * Lung nodule(s) between 0.6-1.0 cm are permitted on study if stable on imaging for least 6 months or if fluorodeoxyglucose-positron emission tomography (FDG-PET) scan suggests that the nodule(s) are low-risk for metastatic disease * Lung nodules \> 1.0 cm should be considered metastatic unless proven otherwise by biopsy or resection or if nodules have stable appearance for at least 6 months on imaging * Any prior surgery (apart from diagnostic biopsy), radiation therapy, or systemic therapy for management of present tumor. Patients with locally recurrent sarcoma after prior surgery alone are eligible for enrollment if other inclusion criteria are met * Hypersensitivity to DOXOrubicin, ifosfamide, mesna, or pembrolizumab or their metabolites or excipients * Prior treatment with DOXOrubicin (or other anthracyclines and anthracenediones) * Clinically significant cardiac disease, including, but not limited to: * Symptomatic congestive heart failure * Angina pectoris * Acute inflammatory heart disease * Myocardial infarction within 1 year before randomization * Uncontrolled cardiac arrhythmia * Active bleeding or clinically significant major bleeding episode within the last 4 weeks * Other invasive malignancy within 2 years, with the exception of adequately treated nonmelanoma skin cancer, localized cervical cancer, or low-risk prostate cancer * Diagnosis of immunodeficiency or treatment with systemic corticosteroids or any other form of systemic immunosuppressive therapy within 7 days prior to study treatment * History of autoimmune disease treated with systemic corticosteroids and/or other disease-modifying agents in the last 2 years * Replacement endocrine therapy (thyroid hormone, insulin, corticosteroids) is not exclusionary * Patients with a history of autoimmune disease previously treated with systemic corticosteroids and/or other disease-modifying agents \> 2 years ago, who are not currently on systemic therapy, may be considered for enrollment on consultation with the medical monitor or study PI * Clinically significant, active, or uncontrolled infection * Known history of active tuberculosis * Active human immunodeficiency virus (HIV) (confirmed by detectable viral load) * Active hepatitis B (confirmed by detectable viral load) * Active hepatitis C (confirmed by detectable viral load) * Any medically significant comorbidity, which in the opinion of the investigator would preclude safe participation in the study