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

Inclusion Criteria: * Patients must have histologically or cytologically confirmed alveolar soft part sarcoma that is not curable by surgery. Diagnosis of malignancy must be confirmed by the department of pathology at the institution where the patient is enrolled prior to patient enrollment. To be eligible for atezolizumab in combination with bevacizumab, the patient must have atezolizumab-refractory/resistant disease that has progressed (definitive clinical progression or confirmed progressive disease \[iCPD\]) on prior 10005 atezolizumab monotherapy * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * Note: Once the primary endpoint of the trial has been met, pediatric patients may enroll with evaluable non-measurable disease and will not be required to have measurable disease. Evaluable non-measurable disease is that which is not measurable by RECIST1.1 but can be evaluated by imaging (e.g., CT, bone scan, or ultrasound) or other methods * Patients with newly diagnosed, unresectable, metastatic and measurable ASPS will also be eligible for atezolizumab monotherapy if they show clinical evidence of disease progression (including history and in…