Testing the Addition of an Anti-Cancer Drug, Cabozantinib to the Immunotherapy Drug Cemiplimab (REGN2810), in Adolescents and Adults With Advanced Adrenocortical Cancer

Inclusion Criteria: * STEP 1: Patients must have documented histologically or cytologically confirmed adrenocortical carcinoma * STEP 1: Locally advanced unresectable or recurrent/metastatic disease * STEP 1: Evaluable disease as defined by RECIST v 1.1 * STEP 1: Up to 3 prior lines of systemic therapy will be allowed in the unresectable/recurrent/metastatic setting. Treatment naïve patients will be allowed. * Note: Combination etoposide, doxorubicin, cisplatin, and mitotane (EDP-M) is considered 1 line of therapy. For patients who received mitotane ≤ 6 months prior to registration, mitotane should be discontinued 28 days prior to study registration AND a mitotane level must be documented to be \< 2 mg/L prior to registration. Patients who have received mitotane within 6 months of enrollment and who have mitotane levels ≥ 2 mg/L will not be eligible to enroll * STEP 1: No prior treatment with cabozantinib or other cMET inhibitors, or anti-CTLA-4, or anti-PD-1/PD-L1 therapy * STEP 1: Prior external beam radiation therapy (any area radiated within a month prior to study registration cannot be used as an index lesion and only growth outside of the radiation field can be considered for disease progression), systemic cytotoxic chemotherapy, targeted therapies will be allowed, as long as not administered within 14 days before study registration, and provided any acute treatment-related associated toxicities have recovered to ≤ grade 1 except for alopecia, peripheral neuropathy or other residual toxicities that are not deemed clinically significant * STEP 1: Potential trial participants should have recovered from clinically significant adverse events, and wound healing is clinically adequate of their most recent therapy/intervention prior to enrollment * STEP 1: Age 12 years and above; and BSA ≥ 1.2m\^2 * STEP 1: * Eastern Cooperative Oncology Group (ECOG) performance 0 - 2 (age 18 and above); or * Patients 12 to \<16 years of age will be assessed by the Lansky scale and should have a score ≥ 50; or * Patients ≥ 16 to \<18 years of age will be assessed by the Karnofsky scale, and should have a score ≥ 50 * STEP 1: Absolute neutrophil count (ANC) ≥ 1,000/mcL without colony stimulating factor support within 2 weeks prior * Transfusion support is allowed if ≥ 7 days from obtaining required initial laboratory * STEP 1: Platelet count ≥ 100,000/mcL * Transfusion support is allowed if ≥ 7 days from obtaining required initial laboratory * STEP 1: Hemoglobin ≥ 8 g/dL * Transfusion support is allowed if ≥ 7 days from obtaining required initial laboratory * STEP 1: Total bilirubin ≤ 1.5 x upper limit of normal (ULN) * For patients with known Gilbert's disease, bilirubin ≤ 3 mg/dL * STEP 1: Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/ alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x upper limit of normal (ULN) * STEP 1: Random Urine Creatinine Ratio (UPCR) ≤ 1 mg/mg * STEP 1: Calculated (Calc.) creatinine clearance ≥ 30 mL/min * STEP 1: Mitotane level \< 2 mg/L\* * Only applicable for patients who have received mitotane ≤ 6 months prior to registration * STEP 1: Must have assessment of adrenal steroid production within 3 months prior to registration as patients will be stratified based on corticosteroid production * Patients will be classified as corticosteroid producing if random plasma adrenocorticotropic hormone (ACTH) is \< 20 pg/mL plus random serum cortisol is \> 20 mcg/dL in the absence of anti-cortisol therapy. Patients already on anti-cortisol therapy will be classified as having corticosteroid producing tumors regardless of their plasma ACTH and serum cortisol levels, as these levels can be affected by anti-cortisol therapy * STEP 1: Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects based on animal reproduction studies. Therefore, for women of childbearing potential only, a negative urine or serum pregnancy test, per institution standard, done ≤ 14 days prior to registration is required * STEP 1: 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 within 28 days of registration. To be eligible for this trial, patients should be class II or better * STEP 1: No known history of congenital long QT syndrome * STEP 1: No known history of myocarditis * STEP 1: No myocardial infarction (MI) or unstable angina within 6 months of registration * STEP 1: No clinically significant gastrointestinal abnormalities that may increase the risk for gastrointestinal bleeding within 6 months of registration including, but not limited to: active peptic ulcer, known endoluminal metastatic lesion(s) with history of bleeding, inflammatory bowel disease, or other gastrointestinal conditions with increased risk of perforation * STEP 1: No history of gastrointestinal (GI) perforation within 6 months of registration * STEP 1: No known tumor with invasion into the GI tract from the outside causing increased risk of perforation or bleeding within 28 days of registration * STEP 1: No current radiologic or clinical evidence of pancreatitis * STEP 1: No history of clinically significant non-healing wounds or ulcers within 28 days of registration * STEP 1: No uncontrolled hypertension within 14 days of registration (defined as sustained systolic blood pressure (SBP) ≥ 150 mmHg and/or diastolic blood pressure (DBP) ≥ 90 mmHg despite optimal medical management) * STEP 1: No known endobronchial lesions involving the main or lobar bronchi and/or lesions infiltrating major pulmonary vessels that increase the risk of pulmonary hemorrhage. (CT with contrast is recommended to evaluate such lesions.). No hemoptysis greater than ½ teaspoon (2.5 mL) or any other signs of pulmonary hemorrhage wit