Doxorubicin and Bevacizumab in Treating Patients With Locally Recurrent or Metastatic Soft Tissue Sarcoma

DISEASE CHARACTERISTICS: * Histologically or cytologically confirmed soft tissue sarcoma * Locally recurrent or metastatic disease * At least 1 unidimensionally measurable lesion * At least 20 mm by conventional techniques OR at least 10 mm by spiral CT scan * No prior or concurrent known brain metastases PATIENT CHARACTERISTICS: Age * 18 and over Performance status * Karnofsky 80-100% OR * ECOG 0-1 Life expectancy * Not specified Hematopoietic * Absolute neutrophil count at least 1,500/mm\^3 * Platelet count at least 100,000/mm\^3 * No bleeding diathesis or coagulopathy Hepatic * Bilirubin no greater than 1.2 mg/dL * AST and ALT no greater than 2.5 times upper limit of normal * PT and aPTT normal Renal * Creatinine no greater than 1.5 mg/dL OR * Creatinine clearance at least 60 mL/min * No proteinuria (must be less than 500 mg protein per 24 hours) Cardiovascular * Cardiac ejection fraction at least 50% by echocardiogram or MUGA * No history of deep vein thrombosis * No clinically significant cardiovascular disease * No uncontrolled hypertension * No myocardial infarction * No unstable angina * No New York Heart Association grade II-IV congestive heart failure * No serious cardiac arrhythmia requiring medication * No grade II or greater peripheral vascular disease within the past year Pulmonary * No history of pulmonary embolism Other * No symptomatic peripheral neuropathy grade 2 or greater * No other neoplastic disease within the past 5 years except curatively treated basal cell skin cancer or carcinoma in situ of the cervix * No prior allergic reactions attributed to compounds of similar chemical or biological composition to bevacizumab (including products derived from Chinese hamster ovary cells), doxorubicin, or dexrazoxane * No HIV-positive patients receiving combination antiretroviral therapy * No ongoing or active infection * No psychiatric illness or social situations that would preclude study entry * No other uncontrolled concurrent illness * No serious, non-healing wound ulcer or bone fracture * No significant traumatic injury within the past 3 weeks * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception PRIOR CONCURRENT THERAPY: Biologic therapy * See Chemotherapy * At least 4 weeks since prior immunotherapy and recovered * No other concurrent immunotherapy Chemotherapy * No prior doxorubicin or any other anthracyclines * No more than 1 prior chemotherapy regimen * The following are not considered prior chemotherapy: * Immunotherapy, including cytokines * Peroxisome-proliferator-activated receptor gamma agonists or thalidomide * At least 4 weeks since prior chemotherapy (6 weeks for carmustine or mitomycin) and recovered * No other concurrent chemotherapy Endocrine therapy * Not specified Radiotherapy * At least 4 weeks since prior radiotherapy and recovered * No concurrent radiotherapy Surgery * At least 3 weeks since prior major surgical procedure or open biopsy * At least 1 week since prior needle biopsy Other * No other concurrent investigational agents * No concurrent full-dose anticoagulants (except to maintain patency of preexisting, permanent indwelling IV catheters) or thrombolytic agent * Concurrent warfarin allowed if INR less than 1.5 * No concurrent chronic daily aspirin (more than 325 mg/day) or nonsteroidal anti -inflammatory medications known to inhibit platelet function * No other concurrent investigational or commercial agents or therapies for this malignancy