The purpose of this study is to find the highest dose of the investigational drug AVA6000 that can be given safely in people with advanced solid tumors that are not responding to treatment. AVA6000 is very similar to a standard chemotherapy drug called doxorubicin. Like doxorubicin, AVA6000 works to slow or stop the growth of cancer cells by blocking an enzyme. Unlike doxorubicin, however, AVA6000 is a "prodrug," meaning it remains inactive until it reaches the site of the cancer. Because of the way AVA6000 works, it may be useful for treating cancer with fewer side effects than doxorubicin. AVA6000 is given intravenously (by vein).