Sorafenib in Treating Patients With Soft Tissue Sarcomas (Extremity Sarcoma Closed to Entry as of 5/30/07)

Inclusion Criteria: * There are two groups of patients eligible for this study; treatment group 1 consists of patients with extremity sarcomas other than potentially curable osteosarcoma or Ewing's sarcoma who are candidates for potentially curative surgery; treatment group 2 consists of patients with metastatic or inoperable sarcoma, for which there is no known curative or survival prolonging palliative therapy, or failure of these therapies; patients must have at least one site of measurable disease by radiologic imaging techniques; patients must have at least one palpable tumor mass with no overlying viscera which is amenable to biopsy; the tumor mass should be approximately 2 cm or greater in diameter; patients with smaller palpable tumors are eligible if participation is approved by the treating surgeon after discussion with the study chairperson * As of 5/30/07, no subjects will accrue to Treatment Group I * Life expectancy \>= 2 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Pretreatment laboratory data, obtained within 14 days of study entry, must meet the following criteria: * Absolute Neutrophil Count (ANC) \>= 1,500/mm\^3 * Platelets \>= 100,000/mm\^3 * Serum glutamic oxaloacetic transaminase (SGOT) =\< 2.5-times the upper limit of normal (ULN) * Serum glutamic-pyruvic transaminase (SGPT)=\< 2.5-times ULN * Total Bilirubin =\< ULN * Serum creatinine =\< 1.5-times ULN * \>= 3 weeks since major surgery unrelated to study disease (sarcoma) * \>= 3 weeks since chemotherapy or radiation therapy (6 weeks for nitrosourea or mitomycin C chemotherapy) * No prior treatment with sorafenib (BAY 43-9006) or specific inhibitors of mitogen-activated protein kinase (MAPK) pathways are permitted; a previously irradiated tumor site cannot be used for clinical or correlative measurements, although irradiation to sites other than a measurable site is permitted; there are no limitations on the extent or type of prior therapy received by the patient other than the time intervals indicated in the above and demonstrating complete recovery from any adverse effects associated by satisfying all relevant eligibility criteria * Patients who are on warfarin anticoagulation are allowed to participate as long as they are converted to a low molecular weight heparin (e.g. lovenox) from study entry until at least day 56 * Women of childbearing potential must not be pregnant or lactating; all women of childbearing potential (age \< 50, last menstrual period \[LMP\] \< 12 months ago) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L of beta-HCG) within 72 hr prior to receiving the study medication; BAY43-9006 has antiproliferative effects, which may be harmful to the developing fetus or nursing infant * Fertile males and females must use adequate contraception * Signed informed consent Exclusion Criteria: * Ewing's sarcoma or osteosarcoma that is potentially curable with surgery, chemotherapy, and/or radiation therapy * Active brain metastases including evidence of cerebral edema by CT scan or MRI, or progression from prior imaging study, any requirements for steroids, or enzyme-inducing anti-convulsant agents, or clinical symptoms of/from brain metastases; patients with treated and/or stable brain metastasis who are asymptomatic can be enrolled, if otherwise eligible * Any uncontrolled serious medical or psychiatric illness; particular note is given to uncontrolled hypertension (discretion left to investigators) and significant proteinuria \> 1 gm/24 hr (does not require quantitation in absence of clinical indication) * Patients receiving other investigational agents * Human immunodeficiency virus (HIV) patients receiving combination anti-retroviral therapy are excluded because of potential pharmacokinetic interactions