This phase II trial studies how well paclitaxel with and without nivolumab works in treating patients with soft tissue sarcoma that have not received taxane drugs, and how well nivolumab and cabozantinib work in treating taxane pretreated patients with soft tissue sarcoma. Nivolumab works through the body's immune system to help the immune system act against tumor cells. Chemotherapy drugs, such as paclitaxel, 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. Cabozantinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. This trial is being done to see if the combination of nivolumab and paclitaxel or cabozantinib can shrink soft tissue sarcoma and possibly prevent it from coming back.