• 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