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.
• 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.
• Patients with newly diagnosed, unresectable, metastatic and measurable ASPS will also be eligible if they show clinical evidence of disease progression (including history and increasing physical symptoms); on-study documentation will include a physician's rationale that supports evidence of clinical disease progression (i.e., increasing tumor pain).
• Age ≥ 2 years at the National Cancer Institute (NCI) clinical center (≥ 14 years at other participating sites).
• Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky or Lansky ≥ 70%).
• Life expectancy of greater than 3 months.
• Leukocytes ≥ 2,500/mcL.
• Absolute neutrophil count ≥ 1,500/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 disease who have serum bilirubin level ≤ 3 x ULN may be enrolled).
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamic pyruvic 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 for adult patients (≥ 18 years of age): ≥ 30 mL/min/1.73 m^2 by Cockcroft-Gault; for pediatric patients (< 18 years of age), a serum creatinine based on age and gender as follows:
  • Age 2 to < 6 years, maximum serum creatinine (mg/dL) male 0.8, female 0.8;
  • Age 6 to < 10 years, maximum serum creatinine (mg/dL) male 1, female 1;
  • Age 10 to < 13 years, maximum serum creatinine (mg/dL) male 1.2, female 1.2;
  • Age 13 to < 16 years, maximum serum creatinine (mg/dL) male 1.5, female 1.4;
  • Age 16 to < 18 years, maximum serum creatinine (mg/dL) male 1.7, female 1.4.
• Administration of atezolizumab may have an adverse effect on pregnancy and poses a risk to the human fetus, including embryo-lethality; female patients of child-bearing potential and male patients must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 5 months (150 days) after the last dose of study agent; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.
• Ability to understand and the willingness to sign a written informed consent document or a parent/guardian able to do the same.
• Willingness to provide biopsy samples for research purposes (patients ≥ 18 years of age only).

Exclusion Criteria:

• Any prior therapy must have been completed ≥ 4 weeks or, if known, ≥ 5 half-lives of the prior agent (whichever is shorter) prior to enrollment on protocol (minimum of 1 week between prior therapy and study enrollment), and the participant must have recovered to eligibility levels from prior toxicity; patients should be at least 6 weeks out from nitrosoureas and mitomycin C; prior definitive radiation should have been completed ≥ 4 weeks or palliative radiation should have been completed ≥ 2 weeks prior to study enrollment and all associated toxicities resolved to eligibility levels (patients on study may be eligible for palliative radiotherapy to non-targeted lesions after 2 cycles of therapy at the principal investigator [PI]'s discretion); patients who have had prior monoclonal antibody therapy must have completed that therapy ≥ 6 weeks (or 3 half-lives of the antibody, whichever is shorter) prior to enrollment on protocol (minimum of 1 week between prior therapy and study enrollment); patients who have received more than a cumulative dose of 350 mg/m^2 of doxorubicin may be enrolled at the discretion of the coordinating center PI, with a screening echocardiogram.
• Prior treatment with anti-PD-1 or anti-PD-L1 therapeutic antibody, or pathway-targeting agents.
• Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met:
  • Minimum of 12 weeks from the first dose of anti-CTLA-4 and > 6 weeks from the last dose;
  • No history of severe immune-related adverse effects from anti-CTLA-4 (NCI Common Terminology Criteria for Adverse Events [CTCAE] grade 3 and 4).
• Treatment with any other investigational agent within 4 weeks (or within five half-lives of the investigational product, whichever is shorter) prior to cycle 1, day 1 (minimum of 1 week between prior therapy and study enrollment); patients must be ≥ 2 weeks since any investigational agent administered as part of a phase 0 study (also referred to as an "early phase I study" or "pre-phase I study" where a sub-therapeutic dose of drug is administered) at the coordinating center PI's discretion, and should have recovered to eligibility levels from any toxicities.
• Treatment with systemic immunostimulatory agents (including, but not limited to, interferon-alpha or interleukin-2 [aldesleukin]) within 6 weeks prior to cycle 1, day 1.
• Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor [anti-TNF] agents) within 2 weeks prior to cycle 1, day 1.
  • Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled.
  • The use of inhaled corticosteroids and systemic mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed.
• Patients taking bisphosphonate therapy for symptomatic hypercalcemia; use of bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is allowed.
• Patients with known primary central nervous system (CNS) malignancy or symptomatic CNS metastases are excluded, with the following exceptions:
  • Patients with asymptomatic untreated CNS disease may be enrolled, provided all of the following criteria are met:
    • Evaluable or measurable disease outside the CNS;
    • No metastases to brain stem, midbrain, pons, medulla, or cerebellum;
    • No history of intracranial hemorrhage or spinal cord hemorrhage;
    • No ongoing requirement for dexamethasone for CNS disease; patients on a stable dose of anticonvulsants are permitted;
    • No neurosurgical resection or brain biopsy within 28 days prior to cycle 1, day 1.
  • Patients with asymptomatic treated CNS metastases may be enrolled, provided all the criteria listed above are met as well as the following:
    • Radiographic demonstration of improvement upon the completion of CNS-directed therapy and no evidence of interim progression between the completion of CNS-directed therapy and radiographic screening for the current study;
    • No stereotactic radiation or whole-brain radiation within 28 days prior to cycle 1, day 1;
    • Screening CNS radiographic study ≥ 4 weeks from completion of radiotherapy and ≥ 2 weeks from discontinuation of corticosteroids.
  • Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies.
• History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies (i.e., antibodies with generic names ending in "ximab" or "zumab", respectively) or fusion proteins.
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
• Pregnant women are excluded from this study because atezolizumab is an investigational agent with the unknown potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with atezolizumab, breastfeeding should be discontinued if the mother is treated with atezolizumab.
• Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible; patients must also have a CD4 count > 350 cells/mm^3 with an undetectable viral load.
• Patients on supraphysiologic doses of steroids or use of such within the previous six weeks.
• Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease.
  • Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible.
  • Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA).
• History or risk of autoimmune disease, including, but not limited to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis:
  • Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible;
  • Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be eligible
    • Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions:
      • Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations;
      • Rash must cover less than 10% of body surface area (BSA);
      • Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%);
      • No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation [PUVA], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids).
• History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.) or evidence of active pneumonitis on screening chest computed tomography (CT) scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted.
• Patients with active tuberculosis (TB) are excluded.
• Severe infections within 4 weeks prior to cycle 1, day 1, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia.
• Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1.
• Received oral or intravenous (IV) antibiotics within 2 weeks prior to cycle 1, day 1; patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible.
• Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of need for a major surgical procedure during the course of the study.
• Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study and up to 5 months after the last dose of atezolizumab:
  • Influenza vaccination should be given during influenza season only (approximately October to March); patients must not receive live, attenuated influenza vaccine within 4 weeks prior to cycle 1, day 1 or at any time during the study.
• Patients requiring treatment with a RANKL inhibitor (e.g., denosumab) who cannot discontinue it before treatment with atezolizumab.