This phase I trial is studying the side effects and best dose of cixutumumab given together with doxorubicin hydrochloride and to see how well they work in treating patients with unresectable, locally advanced, or metastatic soft tissue sarcoma. Monoclonal antibodies, such as cixutumumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Drugs used in chemotherapy, such as doxorubicin hydrochloride, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving monoclonal antibody cixutumumab together with doxorubicin hydrochloride may kill more tumor cells.