Atezolizumab and Cabozantinib for the Treatment of Adolescents and Young Adults With Recurrent or Metastatic Osteosarcoma, TACOS Study

Inclusion Criteria: * Signed informed consent form * Age \>= 12 years at time of signing informed consent form * Ability to comply with the study protocol, in the investigator's judgment * Histologically confirmed diagnosis of osteosarcoma * Metastatic or unresectable locally advanced disease * Patients must have relapsed or become refractory to conventional therapy including some combination of cisplatin, doxorubicin, methotrexate, and/or ifosfamide * Measurable disease per RECIST version (v)1.1 (Note: Previously irradiated lesions can be considered as measurable disease only if progressive disease has been unequivocally documented at that site since radiation) * Availability of a representative tumor specimen for exploratory biomarker research. Archival samples are permitted if the tumor samples been obtained within 6 months prior to enrollment and the patient has not received intervening therapy * A formalin-fixed paraffin-embedded (FFPE) tumor specimen in a paraffin block (preferred) or at least 15 slides containing unstained, freshly cut, serial sections should be submitted along with an associated pathology report prior to study enrollment. If only 10-14 slides are available, the patient may still be eligible for the study, after principal investigator confirmation has been obtained * If archival tumor tissue is unavailable or is determined to be unsuitable for required testing, tumor tissue must be obtained from a biopsy performed at screening * Eastern Cooperative Oncology Group (ECOG) of 0, 1 or 2. Use Karnofsky \>= 50 for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age * Body surface area (BSA) \>= 1 m\^2 * Life expectancy \>= 6 months * Recovery to baseline or =\< grade 1 CTCAE v5 from toxicities related to any prior treatments, unless adverse events (AE\[s\]) are clinically nonsignificant and/or stable on supportive therapy * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L (1000/uL) without granulocyte colony-stimulating factor support (obtained within 14 days prior to initiation of study treatment) * Lymphocyte count \>= 0.5 x 10\^9/L (500/uL) (obtained within 14 days prior to initiation of study treatment) * Platelet count \>= 100 x 10\^9/L (100,000/uL) without transfusion (obtained within 14 days prior to initiation of study treatment) * Hemoglobin \>= 90 g/L (9 g/dL) (obtained within 14 days prior to initiation of study treatment) * Patients may be transfused to meet this criterion * Aspartate aminotransferase (AST), alanine aminotransferase (ALT) =\< 3 x upper limit of normal (ULN) for age (obtained within 14 days prior to initiation of study treatment) * Alkaline phosphatase (ALP) =\< 3 x upper limit of normal (ULN) for age, with the following exceptions: patients with documented bone metastases: ALP =\< 5 x ULN (obtained within 14 days prior to initiation of study treatment) * Serum bilirubin =\< 1.5 x ULN with the following exception: patients with known Gilbert disease: serum bilirubin =\< 3 x ULN (obtained within 14 days prior to initiation of study treatment) * Creatinine clearance \>= 50 mL/min (adults \> 18 years of age, calculated using the Cockcroft-Gault formula) or \>= 50 mL/min/1.73m\^2 (pediatrics patients age 12 - 17, calculated using the Bedside Schwartz equation) (obtained within 14 days prior to initiation of study treatment) * Urine protein/creatinine ratio (UPCR) =\< 1 mg/mg (=\< 113.2 mg/mmol), or 24-hour (h) urine protein =\< 1 g (obtained within 14 days prior to initiation of study treatment) * Serum albumin \>= 20 g/L (2.0 g/dL) (obtained within 14 days prior to initiation of study treatment) * For patients not receiving therapeutic anticoagulation: international normalized ratio (INR) or activated partial thromboplastin (aPTT) =\< 1.5 x ULN (obtained within 14 days prior to initiation of study treatment) * Negative human immunodeficiency virus (HIV) test at screening * Negative hepatitis B surface antigen (HBsAg) test at screening * Women of childbearing potential must not be pregnant at screening. A woman is considered to be of childbearing potential if she is postmenarchal, unless one of the following criteria are met: documented permanent sterilization (hysterectomy, bilateral salpingectomy, or bilateral oophorectomy) or documented postmenopausal status (defined as 12 months of amenorrhea in a woman \> 45 years-of-age in the absence of other biological or physiological causes. In addition, females \< 55 years-of-age must have a serum follicle stimulating \[FSH\] level \> 40 mIU/mL to confirm menopause). Note: documentation may include review of medical records, medical examinations, or medical history interview by study site * For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods as defined below: * Women must remain abstinent or use contraceptive methods with a failure rate of \< 1% per year during the treatment period and for 5 months after the final dose of study treatment with either atezolizumab or cabozantinib * Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices * Hormonal contraceptive methods must be supplemented by a barrier method (including male condom, female condom, or diaphragm with spermicidal gel) * The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not adequate methods of contraception * For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use a condom, and agreement to refrain from donating sperm, as defined below: * With a female partner of childbearing potential or pregnant female partner, men must remain abstinent or use a condom during the treatment period and for 5 months after the final dose of cabozantinib to avoid exposing the embryo. Men must refrain from donating sperm during this same period * The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not adequate methods of preventing drug exposure Exclusion Criteria: * Inability to swallow tablets * Prior treatment with cabozantinib * Prior treatment with immune checkpoint blockade therapies, including anti-CTLA-4, anti-PD-1, and anti-PD-L1 therapeutic antibodies if given in combination with a VEGF-targeted tyrosine kinase inhibitor (TKI). Patients receiving prior anti-PD-1, anti-PD-L1, with or without anti-CTLA-4 antibodies will not be excluded * Receipt of any type of small molecule kinase inhibitor (including investigational kinase inhibitor) within 2 weeks before first dose of study treatment * Receipt of any type of cytotoxic, biologic or other systemic anticancer therapy (including investigational) within 4 weeks before first dose of study treatment * Radiation therapy for bone metastasis within 2 weeks or any other radiation therapy within 4 weeks before first dose of study treatment. Systemic treatment with radionuclides within 6 weeks before first dose of study treatment. Patients with clinically relevant ongoing complications from prior radiation therapy are not eligible * Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks prior to first dose of study treatment after radiotherapy or at least 4 weeks prior to first dose of study treatment after major surgery (e.g., removal or biopsy of brain metastasis). Patients must have complete wound healing from major surgery or minor surgery before first dose of study treatment. Eligible patients must be neurologically asymptomatic and without corticosteroid treatment at the time of first dose of study treatment * History of leptomeningeal disease * Uncontrolled tumor-related pain * Patients requiring pain medication must be on a stable regimen at study entry * Symptomatic lesions (e.g., bone metastases or metastases causing nerve impingement) amenable to palliative radiotherapy should be treated prior to enrollment. Patients should be recovered from the effects of radiation * Asymptomatic metastatic lesions that would likely cause functional deficits or intractable pain with further growth (e.g., epidural metastasis that is not currently associated with spinal cord compression) should be considered for loco-regional therapy if appropriate prior to enrollment * Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently) * Patients with indwelling catheters (e.g., PleurX) are allowed * Concomitant anticoagulation with coumarin agents (e.g., warfarin), direct thrombin inhibitors (e.g., dabigatran), direct factor Xa inhibitor betrixaban, or platelet inhibitors (e.g., clopidogrel). Allowed anticoagulants are the following: * Prophylactic use of low-dose aspirin for cardio-protection (per local applicable guidelines) and low-dose low molecular weight heparins (LMWH) * Therapeutic doses of LMWH or anticoagulation with direct factor Xa inhibitors rivaroxaban, edoxaban, or apixaban in patients without known brain metastases who are on a stable dose of the anticoagulant for at least 1 week before first dose of study treatment without clinically significant hemorrhagic complications from the anticoagulation regimen or the tumor * Uncontrolled or symptomatic hypercalcemia (ionized calcium \> 1.5 mmol/L, calcium \> 12 mg/dL or corrected serum calcium \> upper limit of normal \[ULN\]) * Active or history of autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjogren syndrome, Guillain-Barré syndrome, or multiple sclerosis, with the following exceptions: * Patients with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone are eligible for the study. * Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study. * Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met: * Rash must cover 10% of body surface area * Disease is well controlled at baseline and requires only low-potency topical corticosteroids * No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high-potency or oral corticosteroids within the previous 12 months * History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan * History of radiation pneumonitis in the radiation field (fibrosis) is permitted * Active tuberculosis * Significant cardiovascular disease (such as New York Heart Association Class II or greater cardiac disease, myocardial infarction, or cerebrovascular accident) within 3 months prior to initiation of study treatment, unstable arrhythmia, or unstable angina * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 140 mm Hg systolic or \> 90 mm Hg diastolic (patients \> 13 years of age) or stage 2 hypertension (HTN) as defined by the American Academy of Pediatrics (AAP) as systolic and diastolic BP \>= 95th percentile+12 mmHg, or \>= 140/90 mmHg (whichever is lower, patients \< 13 years of age) despite optimal antihypertensive treatment * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction (MI), or other ischemic event, or thromboembolic event (e.g., deep venous thrombosis, pulmonary embolism) within 6 months before first dose of study treatment * Patients with a diagnosis of incidental, subsegmental pulmonary embolism (PE) or deep vein thrombosis (DVT) within 6 months are allowed if stable, asymptomatic, and treated with a stable dose of permitted anticoagulation (see exclusion criterion) for at least 1 week before first dose of study treatment * Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation * The patient has evidence of tumor invading the GI tract, active peptic ulcer disease, inflammatory bowel disease (e.g., Crohn's disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, acute pancreatitis, acute obstruction of the pancreatic duct or common bile duct, or gastric outlet obstruction * Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose of study treatment * Note: Complete healing of an intra-abdominal abscess must be confirmed before first dose of study treatment * Moderate to severe hepatic impairment (Child-Pugh B or C) * Uncompensated/symptomatic hypothyroidism * Clinically significant hematuria, hematemesis, or hemoptysis of \> 0.5 teaspoon (2.5 ml) of red blood, or other history of significant bleeding (e.g., pulmonary hemorrhage) within 12 weeks before first dose of study treatment * Cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation * Lesions invading or encasing any major blood vessels * Major surgical procedure, other than for diagnosis, within 4 weeks prior to initiation of study treatment, or anticipation of need for a major surgical procedure during the study. Minor surgeries within 10 days before first dose of study treatment. Patients must have complete wound healing from major surgery or minor surgery before first dose of study treatment. Patients with clinically relevant ongoing complications from prior surgery are not eligible * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 500 ms per electrocardiogram (ECG) within 14 days before first dose of study treatment * Note: If a single ECG shows a QTcF with an absolute value \> 500 ms, two additional ECGs at intervals of approximately 3 min must be performed within 30 min after the initial ECG, and the average of these three consecutive results for QTcF will be used to determine eligibility * History of malign