This phase II trial studies how well atezolizumab works in treating patients with non-muscle invasive bladder cancer that has come back (recurrent) and has not responded to treatment (refractory) with Bacillus Calmette-Guerin (BCG). Immunotherapy with monoclonal antibodies, such as atezolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread.

PRIMARY OBJECTIVE: I. To estimate complete response at 25 weeks after registration for those with a carcinoma in situ (CIS) component and to evaluate event-free survival at 18 months in patients with BCG-unresponsive high-risk non-muscle invasive bladder cancer (Ta/T1/CIS) treated with atezolizumab. SECONDARY OBJECTIVES: I. To estimate event-free survival at 18 months for the subset of patients with papillary cancer (Ta/T1). II. To estimate progression-free survival, cystectomy-free survival, bladder cancer-specific survival, overall survival in all patients. ADDITIONAL OBJECTIVES: I. To estimate the level of agreement between local and central pathology review in terms of recurrence (for all patients) and complete response (for the CIS subset). II. To identify markers that predict response to atezolizumab in the CIS population and that are associated with event-free survival (EFS) in patients with Ta/T1/CIS BCG-unresponsive non-muscle invasive bladder cancer. The following markers will be tested: IIIa. Expression of PD-L1 and CD8 by immunohistochemistry (IHC). IIIb. Expression of immune signatures by ribonucleic acid (RNA)-sequencing (RNA-seq). IIIc. Peripheral immune response by mass cytometry (CyTOF) and TruCulture. OUTLINE: Patients receive atezolizumab intravenously (IV) over 60 minutes on day 1. Treatment repeats every 21 days for up to 17 cycles (51 weeks) in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 12 weeks for 2 years and then every 24 weeks for 3 years.