Cabozantinib With Radiation Therapy for the Treatment of Sarcomas of the Extremities

Inclusion Criteria: * Subjects, \>= 18 years old, must have a histologically confirmed diagnosis of sarcomas of the extremities (which may include gluteal muscle involvement) for which neoadjuvant radiation therapy followed by surgical resection is a planned intervention * Subjects whose bowel cannot be completely protected from radiation exposure due to primary tumor location (e.g., proximal lower extremity) will be excluded * Subjects must have one or more measurable target lesions by RECIST version (v) 1.1, assessed via computed tomography (CT) scan or magnetic resonance imaging (MRI) * At the time of study enrollment, subjects must have a tumor burden that is judged to be surgically resectable * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (\>= 1.5 GI/L) without granulocyte colony-stimulating factor support in the last 28 days * White blood cell count \>= 2500/mm\^3 (\>= 2.5 GI/L) * Platelets \>= 100,000/mm\^3 (\>=100 GI/L) without transfusion in the last 28 days * Hemoglobin \>= 9 g/dL (\>= 90 g/L) without transfusion in the last 28 days * Alanine aminotransferase (ALT), aspartate aminotransferase (AST) =\< 3 X upper limit of normal (ULN) * Alkaline phosphatase (ALP) =\< 3 X upper limit of normal (ULN) * ALP =\< 5 X ULN is permitted in subjects with documented bone metastases (phase 1 only) * Total bilirubin =\< 1.5 x ULN (for subjects with Gilbert's disease =\< 3 X ULN) * Serum albumin \>= 2.8 g/dl * Serum creatinine =\< 2.0 x ULN or calculated creatinine clearance \>= 30 mL/min (\>= 0.5 mL/sec) using the Cockcroft-Gault equation * Urine protein/creatinine ratio (UPCR) =\< 1 mg/mg (=\< 113.2 mg/mmol) * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Male or non-pregnant and non-breast feeding female: * Females of child-bearing potential must agree to use highly effective contraception without interruption from initiation of therapy and while on study medication and have a negative serum pregnancy test (beta-human chorionic gonadotropin \[B-hCG\]) result at screening and agree to ongoing pregnancy testing during the study, and at the end of study treatment. A highly effective method of contraception is defined as one that results in a low failure rate (that is, \< 1% per year), when used consistently and correctly, such as implants, injectables, combined oral contraceptives, some intrauterine contraceptive devices, sexual abstinence, or a vasectomized partner * Male subjects must practice abstinence or agree to use a condom during sexual contact with a pregnant female or a female of childbearing potential while participating in the study * Life expectancy of \> 3 months, as determined by the investigator * Ability to understand and sign informed consent * Willingness and ability to comply with scheduled visits, laboratory tests, and other study procedures Exclusion Criteria: * Receipt of any type of cytotoxic, biologic or other systemic anticancer therapy (including investigational) for the investigational diagnosis * Receipt of any prior radiation therapy for the investigational diagnosis * Known central nervous system (CNS) metastases * Concomitant anticoagulation with oral anticoagulants(e.g., warfarin, direct thrombin and factor Xa inhibitors) or platelet inhibitors (e.g., clopidogrel). Allowed anticoagulants are the following: * Low-dose aspirin for cardioprotection (per local applicable guidelines) is permitted * Low-dose low molecular weight heparins (LMWH) are permitted * Anticoagulation with therapeutic doses of LMWH is allowed in subjects without known brain metastases who are on a stable dose of LMWH for at least 6 weeks before first dose of study treatment, and who have had no clinically significant hemorrhagic complications from the anticoagulation regimen or the tumor. Subjects with hemoptysis, central nervous system hemorrhage or gastrointestinal hemorrhage within the last 6 months prior to treatment are excluded * The subject has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Cardiovascular disorders: * Congestive heart failure New York Heart Association Class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 150 mm Hg systolic or \> 100 mm Hg diastolic despite optimal anti-hypertensive treatment * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction (MI), or other ischemic event, or thromboembolic event (e.g., deep venous thrombosis, pulmonary embolism) within 6 months before first dose. * Uncontrolled serious medical or psychiatric illness * Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation: * The subject has evidence of tumor invading the GI tract, active peptic ulcer disease, inflammatory bowel disease (e.g., Crohn's disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, acute pancreatitis, acute obstruction of the pancreatic duct or common bile duct, or gastric outlet obstruction * Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose * Note: Complete healing of an intra-abdominal abscess must be confirmed before first dose * Clinically significant hematuria, hematemesis, or hemoptysis of \> 0.5 teaspoon (2.5 ml) of red blood, or other history of significant bleeding (e.g., pulmonary hemorrhage) within 12 weeks before first dose * Cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation * Lesions invading or encasing any major blood vessels * Other clinically significant disorders that would preclude safe study participation * Serious non-healing wound/ulcer/bone fracture * Uncompensated/symptomatic hypothyroidism * Moderate to severe hepatic impairment (Child-Pugh B or C) * Major surgery (e.g., GI surgery, removal or biopsy of brain metastasis) within 8 weeks before first dose of study treatment. Complete wound healing from major surgery must have occurred at least 30 days before first dose, and from minor surgery (e.g., simple excision, tooth extraction) at least 10 days before first dose. Subjects with clinically relevant ongoing complications from prior surgery are not eligible * Corrected QT interval calculated by the Bazett's formula (corrected QT \[QTc\]) \> 480 ms per electrocardiogram (ECG) within 28 days before first dose of study treatment * Note: If a single ECG shows a QTc with an absolute value \> 480 ms, two additional ECGs at intervals of approximately 3 min must be performed within 30 min after the initial ECG, and the average of these three consecutive results for QTc will be used to determine eligibility * Pregnant or lactating females * Inability to swallow tablets * Previously identified allergy or hypersensitivity to components of the study treatment formulations * Diagnosis of another malignancy within 2 years before first dose of study treatment, except for superficial skin cancers, or localized, low-grade tumors deemed cured and not treated with systemic therapy * Concurrent use of medications (especially those interacting with CYP3A417) that potentially interact unsafely with cabozantinib which cannot be discontinued or substituted * Subjects with a sarcoma which has other, defined treatments or biology distinctly different from those of soft tissue sarcomas in general. Including, but not limited to, Ewing's sarcoma, rhabdomyosarcoma, gastrointestinal stromal tumors, Kaposi's sarcoma, Wilms' tumor * Transfusion of blood product or granulocyte-colony stimulating factor (G-CSF) support factor within the last 28 days * Recent infection requiring systemic anti-infective treatment that was completed =\< 14 days prior to enrollment (except for uncomplicated urinary tract infection or upper respiratory tract infection)