This phase II trial studies how well giving azacitidine and entinostat work in treating patients with advanced breast cancer. Drugs used in chemotherapy, such as azacitidine, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Entinostat may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving azacitidine together with entinostat may kill more tumor cells.