This phase I/II trial studies the side effects and best dose of eribulin mesylate and to see how well it works in treating patients with cancer of the urothelium that has spread to nearby tissue or to other places in the body and kidney dysfunction. Drugs used in chemotherapy, such as eribulin mesylate, 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. Chemotherapy drugs may have different effects in patients who have changes in their kidney function.