This phase II trial studies how well recombinant EphB4-HSA fusion protein and pembrolizumab work in treating patients with urothelial (bladder) cancer that has spread from the primary site to other places in the body or has come back and does not respond to certain chemotherapy drugs. Combinations of biological substances in recombinant EphB4-HSA fusion protein may be able to carry tumor-killing substances directly to urothelial cancer cells. Monoclonal antibodies, such as pembrolizumab, may interfere with the ability of cancer cells to grow and spread. Giving recombinant EphB4-HSA fusion protein and pembrolizumab together may be a better treatment for patients with urothelial cancer.