Atezolizumab and CYT107 in Treating Participants With Locally Advanced, Inoperable, or Metastatic Urothelial Carcinoma

Inclusion Criteria: * Patients must have histologically or cytologically documented locally advanced/inoperable or metastatic urothelial bladder carcinoma (UBC), including renal pelvis, ureters, urinary bladder, and urethra * Note: Mixed histology tumors allowed if predominant histology is urothelial carcinoma * Note: Small cell or neuroendocrine carcinoma is not allowed if predominant * Patients must have recurrent disease after any prior platinum-based chemotherapy regimen * Patients must have measurable disease per RECIST 1.1 assessed by computed tomography (CT) scan or magnetic resonance imaging (MRI) * ECOG performance status =\< 2 (Karnofsky \>= 60%) * Patients must have a life expectancy of greater or equal to 12 weeks * Leukocytes \>= 2,500/mcL * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 8 g/dL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (however, patients with known Gilbert's disease who have serum bilirubin level =\< 3 x ULN may be enrolled) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN (AST and/or ALT=\< 5 x ULN for patients with liver involvement) * Alkaline phosphatase =\< 2.5 x ULN (=\< 5 x ULN for patients with documented liver involvement or bone metastases) * Creatinine clearance \>= 30 mL/min/1.73 m\^2 by Cockcroft-Gault * At the discretion of the trea…