Testing Atezolizumab Alone or Atezolizumab Plus Bevacizumab in People With Advanced Alveolar Soft Part Sarcoma

PRIMARY OBJECTIVES: I. Determine the objective response rate (ORR) using Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 of atezolizumab in patients with advanced alveolar soft part sarcoma (ASPS) in adult subjects \>= 18 years and in pediatric/adolescent subjects \>= 2 years. II. Determine the ORR using RECIST v 1.1 of atezolizumab and bevacizumab in subjects \>= 18 years old with advanced ASPS that has progressed on atezolizumab monotherapy. SECONDARY OBJECTIVES: I. Determine duration of response (DOR) to atezolizumab monotherapy or atezolizumab plus bevacizumab using RECIST v 1.1 and/or change in clinical symptoms. II. Measure progression-free survival (PFS) time for patients receiving atezolizumab monotherapy or atezolizumab plus bevacizumab as determined by investigator using RECIST v 1.1. III. Assess the number of activated CD8+ T cells infiltrating the tumor before and after treatment with atezolizumab monotherapy or atezolizumab plus bevacizumab, and correlate treatment-induced changes with clinical response. IV. Measure and describe the atezolizumab pharmacokinetics (PK) and anti-drug antibodies (ADA) in patients ages 2-11 years old. EXPLORATORY OBJECTIVES: I. Compare RECIST v 1.1 vs immune RECIST (iRECIST) in patients with ASPS on atezolizumab and atezolizumab + bevacizumab. II. Assess the post-progression response rate among patients who progress while on treatment holiday and then resume treatment. III. Analyze the genomic and immune profiles of tumors expressing type 1 or type 2 ASPL-TFE3 fusions and correlate findings with response to atezolizumab or atezolizumab in combination with bevacizumab. IV. Measure and describe the atezolizumab pharmacokinetics (PK) in patients \>= 12 years old. OUTLINE: Patients are assigned to 1 of 2 arms. ARM I: Patients receive atezolizumab intravenously (IV) over 30-60 minutes on day 1 of each cycle. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. Patients in arm I who do achieve disease progression may cross-over to arm II. Patients also undergo computed tomography (CT) imaging, and collection of blood and urine at baseline. (CLOSED TO ACCRUAL) ARM II: Patients receive atezolizumab IV over 30-60 minutes and bevacizumab IV over 30-90 minutes on day 1 of each cycle. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. Patients also undergo CT imaging, and collection of blood and urine at baseline. After completion of study treatment, patients are followed up for 27-30 days. Patients who are progression-free at the end of a 2-year treatment holiday are followed every 6 months.