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