This phase III trial compares the effect of cisplatin or carboplatin (platinum-based chemotherapy) to capecitabine after initial chemotherapy (neoadjuvant therapy) followed by surgery for the treatment of residual triple-negative breast cancer. Chemotherapy drugs, such as cisplatin, carboplatin, and capecitabine, 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. At present, upon completion of chemotherapy and surgery, the standard of care for patients with triple-negative breast cancer is observation. However, recent studies have shown that giving capecitabine after completion of chemotherapy and surgery is a better treatment than receiving no treatment and also that platinum-based chemotherapy after neoadjuvant therapy and surgery may prevent residual triple-negative breast cancer from returning. This trial compares the benefit of adding a platinum agent vs. capecitabine to the treatment regimen, following completion of neoadjuvant therapy and surgery in patients with residual triple-negative breast cancer. Eligibility includes being at least 18 years old, Stage II-III, ER, PR, and HER2 negative, completed neoadjuvant chemotherapy that includes a Taxane and surgery. Other eligibility requirements are necessary and can be discussed with the clinical trials coordinator if interested.