This randomized phase II trial studies how well cisplatin works with or without veliparib in treating patients with triple-negative breast cancer and/or BRCA mutation-associated breast cancer that has come back (recurrent) or has or has not spread to the brain (brain metastases). Drugs used in chemotherapy, such as cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. PARPs are proteins that help repair DNA mutations. PARP inhibitors, such as veliparib, can keep PARP from working, so tumor cells can't repair themselves, and they may stop growing. It is not yet known if cisplatin is more effective with or without veliparib in treating patients with triple-negative and/or BRCA mutation-associated breast cancer.