This phase III trial compares the usual chemotherapy treatment to eribulin plus gemcitabine in treating patients with urothelial cancer that has spread to other places in the body (metastatic). Chemotherapy drugs, such as eribulin, gemcitabine, docetaxel, paclitaxel, and sacituzumab govitecan 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. This trial aims to see whether adding eribulin to standard of care chemotherapy may work better in treating patients with metastatic urothelial cancer.