Atezolizumab and Bevacizumab in Treating Patients With Rare Solid Tumors

Inclusion Criteria: * Signed informed consent form * Ability to comply with the study protocol, in the investigator's judgment * Measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1; previously irradiated lesions can be considered as measurable disease only if progressive disease has been unequivocally documented at that site since radiation; the pleural mesothelioma cohort will require measurable disease according to modified RECIST * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L without granulocyte colony-stimulating factor support, obtained within 14 days prior to initiation of study treatment * Lymphocyte count \>= 0.5 x 10\^9/L, obtained within 14 days prior to initiation of study treatment * Platelet count \>= 100 x 10\^9/L without transfusion, obtained within 14 days prior to initiation of study treatment * White blood cell (WBC) count \>= 2500/ul, obtained within 14 days prior to initiation of study treatment * Hemoglobin \>= 90 g/L (patients may be transfused to meet this criterion), obtained within 14 days prior to initiation of study treatment * Aspartate aminotransferase (AST), alanine aminotransferase (ALT), and alkaline phosphatase (ALP) =\< 2.5 x upper limit of normal (ULN), obtained within 14 days prior to initiation of study treatment, with the following exceptions: patients with documented liver metastases: AST and ALT =\< 5 x ULN; p…