Yttrium Y 90 Glass Microspheres, Atezolizumab, and Cabozantinib for the Treatment of Unresectable or Locally Advanced Hepatocellular Carcinoma

Inclusion Criteria: * Participant must provide written informed consent before any study-specific procedures or interventions are performed * Participants aged \>= 18 years * Capable of understanding and complying with the protocol requirements and must have signed the informed consent document * Patients must have histologically or cytologically confirmed hepatocellular cancer that is not amenable to transplant or resection: * Barcelona Clinic Liver Cancer Stage B or C * Cirrhosis grade of Child-Pugh class A * Fibrolamellar and mixed hepatocellular/cholangiocarcinoma subtypes are not eligible * Disease must not be amenable to surgical resection, transplantation, or thermal ablation, or recurrent hepatocellular carcinoma (HCC) after a previous definitive therapy (surgery or thermoablative therapy) * Venous invasion (portal, hepatic, inferior vena cava \[IVC\], biliary) and infiltrative growth pattern are eligible * Eastern Cooperative Oncology Group (ECOG) 0 - 1 * Recovery to baseline or =\< grade 1 (per Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\]5.0) from toxicities related to any prior treatments, unless adverse events (AE\[s\]) are clinically non-significant and/or stable on supportive therapy * Hemoglobin \>= 9 g/dL (\>= 90 g/L) (within 14 days before first dose of study treatment) * White blood cell count \>= 2500/uL (within 14 days before first dose of study treatment) * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (1500/uL), without granulocyte colony-stimulating factor (GSF) support (within 14 days before first dose of study treatment) * Platelet count \>= 60 x 10\^9/L (\>= 60,000/uL), without transfusion (within 14 days before first dose of study treatment) * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 5 x upper limit of normal (ULN) (within 14 days before first dose of study treatment) * Alkaline phosphatase (ALP) =\< 5 x ULN (within 14 days before first dose of study treatment) * Total bilirubin =\< 2 mg/dL (=\< 34.2 umol/L) (within 14 days before first dose of study treatment) * Serum albumin \>= 2.8 g/dL (within 14 days before first dose of study treatment) * Prothrombin time/international normalized ratio (PT/INR) or partial thromboplastin time (PTT) test \< 1.3 x laboratory ULN (within 14 days before first dose of study treatment) * Serum creatinine =\< 1.5 x ULN or calculated creatinine clearance \>= 40 mL/min (\>= 0.675 mL/sec) using the Cockcroft-Gault equation (within 14 days before first dose of study treatment) * Urine protein/creatinine ratio (UPCR) =\< 1 mg/mg (=\< 113.2 mg/mmol), or 24-hour (h) urine protein =\< 1 g (within 14 days before first dose of study treatment) * Has at least one measurable lesion based on Modified Response Evaluation Criteria in Solid Tumors (mRECIST) * Eligible for Y-90 radioembolization based on planning angiogram and evidence of \>= 30% hepatic reserve (untreated background liver) * Participants must have at least one measurable site of disease as defined by mRECIST that is amendable to biopsy * Must agree to undergo 2 mandatory on-study tumor biopsies (at time of Y-90 radioembolization and after completing the initial combination cycle of atezolizumab and cabozantinib). A third on-study biopsy at time of disease progression is optional but not mandatory * Sexually active fertile participants and their partners must agree to use medically accepted methods of contraception (e.g., barrier methods, including male condom, female condom, or diaphragm with spermicidal gel) during the course of the study and for 4 months after the last dose of cabozantinib and 5 months after the last dose of atezolizumab * Participants of childbearing potential must not be pregnant at screening. Participants are considered to be of childbearing potential unless one of the following criteria is 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 * Participants \< 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 Exclusion Criteria: * Another primary tumor * Extrahepatic metastases * Advanced liver disease with a Child-Pugh B or C, or active gastrointestinal bleeding or encephalopathy or refractory ascites * Prior systemic therapy for HCC * Prior Y-90 radioembolization. Prior chemoembolization is permitted * 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. Subjects with clinically relevant ongoing complications from prior radiation therapy are not eligible * Prior treatment with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent, or with an agent directed to another co-inhibitory T-cell receptor (e.g. CTLA-4, OX-40, and CD137). Note: Patients who have received their first dose of atezolizumab as a first-line treatment of their HCC no longer than 21 days from signing consent, may still be eligible * Prior treatment with cabozantinib * Receipt of any type of small molecule kinase inhibitor (including investigational kinase inhibitor) within 2 weeks before first dose of study treatment * Participants cannot be on other forms of anti-cancer therapy at the same time, except as described within this protocol * Concomitant anticoagulation with coumarin agents (e.g., warfarin), direct thrombin inhibitors (e.g., dabigatran), direct factor Xa inhibitors (e.g., rivaroxaban), 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 in participants with a screening platelet count \> 100,000/uL, without known brain metastases, and 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 * Participant has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Cardiovascular disorders: * Congestive heart failure New York Heart Association class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 140 mm Hg systolic or \> 90 mm Hg diastolic 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 * Participants 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 for at least 1 week before start of study intervention * Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation: * Participant 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 * Gastric or esophageal varices that are untreated or incompletely treated with bleeding or high risk for bleeding. Participants treated with adequate endoscopic therapy (according to institutional standards) without any episodes of recurrent GI bleeding requiring transfusion or hospitalization for at least 6 months prior to study entry are eligible * 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 start of study intervention * Elevated lung shunting precluding safe treatment with Y-90 within acceptable thresholds of lung exposure (\< 30 Gy/treatment; \< 50 Gy total) * Patients with anticipated \< 30% liver reserve after Y-90 treatment * Patients in whom Y-90 is deemed unsafe due to risks of extra-pulmonary non-target embolization * Patients with renal failure currently requiring dialysis of any kind are not eligible * Cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation * Lesions invading or encasing any major blood vessels. Participants with lesions invading the intrahepatic vasculature, including portal vein, hepatic vein, and hepatic artery, are eligible * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins * Known hypersensitivity or allergy to biopharmaceuticals produced in Chinese hamster ovary cells or to any component of the atezolizumab formulation * Other clinically significant disorders that would preclude safe study participation * Any active, known or suspected autoimmune disease will be excluded, with the following exceptions: * Type 1 diabetes mellitus * Hypothyroidism only requiring hormone replacement * Skin disorders (e.g., vitiligo, psoriasis, or alopecia) not requiring systemic treatment * Conditions not expected to recur in the absence of an external trigger * Any condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days before first dose of study treatment * Inhaled, intranasal, intra-articular, or topical steroids are permitted. Adrenal replacement steroid doses \> 10 mg daily prednisone equivalent are permitted. Transient short-term use of systemic corticosteroids for allergic conditions (e.g., contrast allergy) is also allowed * This criteria may be waived per investigator discretion for patients who have received 1 dose of atezolizumab per standard of care prior to consenting to this trial * Patients with a history of allergic reaction to IV contrast requiring steroid pre-treatment should have screening and subsequent tumor assessments performed using magnetic resonance imaging (MRI) * Active infection requiring systemic treatment including acquired immunodeficiency syndrome (AIDS)-related illness, or known positive test for tuberculosis infection where there is clinical or radiographic evidence of active mycobacterial infection. Exceptions to this are as follows: * Patient has controlled infection by hepatitis B virus (HBV), defined as receiving effective antiviral therapy and have a viral load less than 100 IU/mL. Must meet liver function inclusion parameters stated above (i.e., ALT, AST, bilirubin) * Patient has infection by hepatitis C (HCV). Participants with active, uncontrolled HCV infection are eligible provided liver function meets eligibility criteria and are receiving management of the disease per local institutional practice * Human immunodeficiency virus (HIV)-infected participants on effective anti-retroviral therapy with undetectable viral load for \>= 6 months are eligible for this trial provided that there is minimal interactions or overlapping toxicity of the antiretroviral therapy with their study intervention. Participants with active infection requiring systemic treatment, infection with HIV or acquired immunodeficiency syndrome (AIDS)-related illness are not eligible for participation * History of idiopathic pulmonary fibrosis, organizing pneumonia, drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan * Serious non-healing wound/ulcer/bone fracture * Malabsorption syndrome * Uncompensated/symptomatic hypothyroidism * Requirement for hemodialysis or peritoneal dialysis * History of solid organ or allogenic stem cell transplant * Prior allogeneic stem cell or solid organ transplantation * Receipt of a live, attenuated vaccine within 4 weeks prior to enrollment or anticipation that a live, attenuated vaccine will be required during atezolizumab treatment or within 5 months after the last dose of atezolizumab * Treatment with systemic immunostimulatory agents (including but not limited to interferons or interleukin \[IL\]-2) within 4 weeks or five half-lives of the drug (whichever is longer) prior to start of study intervention * Poor peripheral venous access * Evidence of significant uncontrolled concomitant disease that could affect compliance with the protocol, safety of participation, or interpretation of results. This includes significant liver disease (such as cirrhosis, uncontrolled major seizure disorder, or superior vena cava syndrome) or any other serious medical condition or abnormality in clinical laboratory tests that meet these criteria in the investigator's opinion * Major surgery (e.g., laparoscopic nephrectomy, GI surgery, removal or biopsy of brain metastasis) within 2 weeks before first dose of study treatment. Minor surgeries within 10 days before first dose of study treatment. Participants must have complete wound healing from major surgery or minor surgery before first dose of study treatment. Participant 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. Furthermore, participants with a history of additional risk factors for torsades de pointes (e.g., long QT syndrome) are also excluded * Note: If a single ECG shows a QTcF with an absolute value \> 500 ms, two additional ECGs at intervals of approximately 3 minutes (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 * Patient is pregnant or lactating * Inability to swallow tablets or unwillingness or inability to receive IV administration * Previously identified allergy or hypersensitivity to the study agents or their excipients or components, or history of severe infusion-related reactions to monocl