This phase II trial studies how well brostallicin and cisplatin work in treating patients with breast cancer that has spread to other parts of the body (metastatic) and does not have estrogen receptors, progesterone receptors, or large amounts of human epidermal growth factor receptor 2 (HER2) on its cells (triple-negative). Drugs used in chemotherapy, such as brostallicin and cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from spreading.