Pazopanib Hydrochloride Followed by Chemotherapy and Surgery in Treating Patients With Soft Tissue Sarcoma

Inclusion Criteria: * Histologically or cytologically confirmed soft-tissue sarcoma, excluding alveolar and embryonal rhabdomyosarcoma, well- and dedifferentiated adipocytic sarcomas, Ewing's, osteosarcoma, or gastrointestinal stromal tumor; American Joint Committee on Cancer (AJCC) (6th Edition) Stage III or T2a Stage II or Stage IV treatment naive patients planned for resection of the primary tumor, with resectable metastatic disease * Measurable disease greater than 5 centimeters in greatest dimension; measurable lesions are defined as those that can be accurately measured in at least one dimension (longest diameter for non-nodal lesions and short axis for nodal lesions to be recorded) by chest x-ray, computed tomography (CT) scan, magnetic resonance imaging (MRI) or with calipers by clinical exam; all tumor measurements must be recorded in millimeters (or decimal fractions of centimeters) * Intermediate or high grade lesions: 2 or 3 on a scale of 1-3 or grades 2 to 4 on a scale of 1-4 * Sarcoma located on upper (includes shoulder) or lower (includes hip) extremities or on the body wall * Life expectancy of greater than 6 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Karnofsky \>= 80% * No prior chemotherapy, radiotherapy, or antiangiogenic therapy * Absolute neutrophil count (ANC) \>= 1500/uL * Hemoglobin (Hgb) \>= 9.0 g/dL * Platelets \>= 100,000/uL * Creatinine =\< 1.5 x upper limit of normal (ULN) * Bilirubin =\< 1.5 mg/dL * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 1.5 x ULN * Prothrombin time (PT)/international normalized ratio (INR)/partial thromboplastin time (PTT) within 1.2 X the ULN unless a subject is receiving Coumadin and has stable INR which is in range for the desired level of anticoagulation * Left ventricular ejection fraction (LVEF) \>= 50% * Blood pressure (BP) no greater than 140 mmHg (systolic) and 90 mmHg (diastolic) for eligibility; initiation or adjustment of BP medication is permitted prior to study entry provided that the average of three BP readings on baseline assessment prior to enrollment is less than 140/90 mmHg * Eligibility of subjects receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of pazopanib will be determined following review of their cases by the Principal Investigator * Women of child-bearing potential and men must agree to use adequate contraception * A female is eligible to enter and participate in this study if she is of non-childbearing potential (i.e., physiologically incapable of becoming pregnant) or if she is of childbearing potential * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Subjects with known brain metastases and/or unresectable sarcoma * Uncontrolled intercurrent illness including, active serious infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac ventricular arrhythmia requiring anti-arrhythmic therapy, serious hepatic impairment, or psychiatric illness/social situations that would limit compliance with study * Pregnant or lactating women * Subjects with no additional active malignancy within the last 3 years * Subjects receiving other investigational agents * Subjects with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to pazopanib or other agents used in the study * Subjects who have both bilirubin \> ULN and AST/ALT \> ULN * Subjects with a urine protein/creatinine ratio greater than 1 * Subjects with a baseline corrected QT (QTc) of equal to or greater than 480 msecs or other significant electrocardiogram (ECG) abnormalities * Certain medications that act through the cytochrome P450 (CYP450) system are specifically prohibited in subjects receiving pazopanib and others should be avoided or administered with extreme caution and require principal investigator (PI) approval * Strong inhibitors of CYP3A4 such as ketoconazole, itraconazole, clarithromycin, atazanavir, indinavir, nefazodone, nelfinavir, ritonavir, saquinavir, telithromycin, voriconazole may increase pazopanib concentrations and are prohibited; grapefruit juice is also an inhibitor of CYP450 and should not be taken with pazopanib * Strong inducers of CYP3A4, such as rifampin, may decrease pazopanib concentrations, are prohibited * Medications which have narrow therapeutic windows and are substrates of CYP3A4, CYP2D6, or CYP2C8 should be avoided and, if necessary, administered with caution * Pazopanib, 800 mg once daily, has no effect on CYP2C9, CYP1A2, or CYP2C19 in vivo but does in vitro; therefore, therapeutic doses of warfarin, a substrate of CYP2C9, and omeprazole, a substrate of CYP2C19 are permitted; caffeine, a substrate of CYP1A2, is also permitted * Certain medications that are associated with a risk for QTc prolongation and/or Torsades de Pointes, although not prohibited, should be avoided or replaced with medications that do not carry these risks, if possible * Subjects who require heparin other than low-molecular weight heparin * Subjects with any condition that may impair the ability to swallow or absorb oral medications/investigational product including: * Any lesion, whether induced by tumor, radiation or other conditions, which makes it difficult to swallow capsules or pills * Prior surgical procedures affecting absorption including, but not limited to major resection of stomach or small bowel * Active peptic ulcer disease, not on a proton pump inhibitor * Malabsorption syndrome * Subjects with any condition that may increase the risk of gastrointestinal bleeding or gastrointestinal perforation, including * Active peptic ulcer disease, not on a proton pump inhibitor * Known intraluminal metastatic lesions * Inflammatory bowel disease (e.g., ulcerative colitis, Crohn's disease) or * Other gastrointestinal conditions which increase the risk of perforation * History of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 28 days prior to beginning study treatment * Subjects with any of the following cardiovascular conditions within the past 6 months: * Cerebrovascular accident (CVA) or transient ischemic attack (TIA) * Cardiac arrhythmia * Admission for unstable angina * Cardiac angioplasty or stenting * Coronary artery bypass graft surgery * Pulmonary embolism, untreated deep venous thrombosis (DVT) or DVT which has been treated with therapeutic anticoagulation for less than 6 weeks * Arterial thrombosis * Symptomatic peripheral vascular disease * Class III or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system; a subject who has a history of Class II heart failure and is asymptomatic on treatment may be considered eligible * History of hemoptysis in excess of 2.5 mL (1/2 teaspoon ) within 8 weeks prior to first dose of study drug * History of serious or non-healing wound, ulcer, or bone fracture * Human immunodeficiency virus (HIV)-positive subjects on combination antiretroviral therapy are ineligible * Subjects with severe hepatic impairment * Bilirubin \> 3 x ULN, regardless of any level of ALT