Additional Study Information: The purpose of this study is to evaluate the effectiveness of a new investigational drug, ATX-101, for the treatment of dedifferentiated liposarcoma and leiomyosarcoma. ATX-101 is an intravenous (IV) drug which blocks the interaction of a protein called PCNA with a number of stress response proteins. These interactions are thought to be important for cancer cell survival and growth. ATX-101 may disrupt these interactions and therefore help treat the cancer. In this study, all patients will receive the same treatment. Most of the exams, tests, and procedures you will have are part of the usual approach to medical care for your condition. However, some additional tests or procedures may be performed, and other tests may be performed more frequently than usual.