Testing Atezolizumab in People 2-17 Years Old With Clear Cell Sarcoma or Advanced Chondrosarcoma

Inclusion Criteria: * Patients must have documented EWSR1/ATF1 or EWSR1/CREB1 translocation or histologically confirmed clear cell sarcoma, documented grade 2 or 3 conventional chondrosarcoma, or documented dedifferentiated chondrosarcoma. The disease must not be curable by surgery * 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 clear cell sarcoma, EWSR1/ATF1 or EWSR1/CREB1 translocation, grade 2 or 3 conventional chondrosarcoma, or dedifferentiated chondrosarcoma 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 (\>= 12 years at other participating sites) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky or Lansky \>= 70%) * Life expectancy of greater than 3 months * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 8 g/dL * Total bilirubin =\< 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 glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional 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: * 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): 0.8 (male) 0.8 (female) * Age: 6 to \< 10 years; Maximum serum creatinine (mg/dL): 1 (male) 1 (female) * Age: 10 to \< 13 years; Maximum serum creatinine (mg/dL): 1.2 (male) 1.2 (female) * Age: 13 to \< 16 years; Maximum serum creatinine (mg/dL): 1.5 (male) 1.4 (female) * Age: 16 to \< 18 years; Maximum serum creatinine (mg/dL): 1.7 (male) 1.4 (female) * Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression for \>= 1 month after treatment of the brain metastases * Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS-specific treatment is not required and is unlikely to be required during the first 2 cycles of therapy * Patients with a prior malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better * Willingness to provide biopsy samples for research purposes (patients \>= 18 years of age only) * 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 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). A patient who has received a cumulative dose of \> 350 mg/m\^2 of anthracycline (regardless of cardioprotectant) may only be enrolled if their ejection fraction measured by an echocardiogram is within normal institutional limits * 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 \[ \> 10 mg/day\], 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 * 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 * Patients with a history of human immunodeficiency virus (HIV)-positive on antiretroviral therapy are eligible with an undetectable viral load. For those patients, an HIV viral load test must be completed within 28 days prior to enrollment * 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 autoimmune hyperthyroid disease not requiring immunosuppressive treatment 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, or 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