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 or has or has not spread to the brain. 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. Veliparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. 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.