Doxorubicin Hydrochloride and Alvocidib in Treating Patients With Metastatic or Recurrent Sarcoma That Cannot Be Removed By Surgery

Inclusion Criteria: * Histologically or cytologically confirmed soft-tissue sarcoma\* * Unresectable disease * Locally recurrent or metastatic disease * Disease amenable to biopsy (patients treated at the maximum tolerated dose only) * No known prior or concurrent brain metastases * Performance status - Karnofsky 60-100% * Performance status - ECOG 0-2 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Bilirubin ≤ 1.5 mg/dL * AST and ALT ≤ 2.5 times upper limit of normal * Creatinine ≤ 1.5 mg/dL * Creatinine clearance ≥ 60 mL/min * Ejection fraction ≥ 50% by MUGA or echocardiogram * No uncontrolled hypertension * No myocardial infarction * No New York Heart Association class II-IV congestive heart failure * No unstable angina * No serious cardiac arrhythmia requiring medication * No peripheral vascular disease ≥ grade 2 within the past year * No other clinically significant cardiac disease * No prior deep vein thrombosis * No other prior vascular thrombus * No prior pulmonary embolism * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No symptomatic peripheral neuropathy ≥ grade 2 * No other malignancy within the past 5 years except adequately treated basal cell skin cancer or carcinoma in situ of the cervix * Carcinoma in situ not considered a second malignancy * No history of allergic reaction attributed to compounds of similar chemical or biologic composition to study drugs * No psychiatric illness or social situation that would preclude study compliance * No ongoing or active infection * No other uncontrolled illness * See Chemotherapy * At least 3 weeks since prior immunotherapy and recovered * At least 3 weeks since prior chemotherapy (6 weeks for carmustine or mitomycin) and recovered * No more than 2 prior cytotoxic chemotherapy regimens * Peroxisome proliferator-activated receptor (PPAR)-gamma agonists, thalidomide, or targeted therapy (i.e., tyrosine kinase inhibitors including imatinib mesylate, sorafenib, or sunitinib malate) do not count as a prior chemotherapy regimen * No prior anthracyclines * At least 3 weeks since prior radiotherapy and recovered * No prior extensive radiotherapy to bone marrow-producing sites (e.g., radiotherapy to both the pelvis and spine) * At least a 1 week washout period since prior tyrosine kinase inhibitors or other targeted therapy * Concurrent low-dose warfarin (1 mg per day) to prevent thrombus of a central line allowed * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent investigational agents * No other concurrent anticancer therapy