Atezolizumab in Combination With a Multi-Kinase Inhibitor for the Treatment of Unresectable, Locally Advanced, or Metastatic Liver Cancer

Inclusion Criteria: * Provide written informed consent =\< 28 days prior to randomization * Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) * NOTE: During the Active Monitoring Phase of a study (i.e., active treatment and clinical follow-up), participants must be willing to return to the consenting institution for follow-up * Age \>= 18 years * Hepatocellular carcinoma (HCC) confirmed by histological/cytological diagnosis or clinically per the American Association for the Study of Liver Diseases (AASLD) or WASL 2018 criteria * Locally advanced, metastatic and/or unresectable disease that is not amendable to curative treatment * Previously progressed on atezolizumab in combination with bevacizumab as first line systemic therapy for advanced disease * NOTE: 2nd line patients only * Eastern Cooperative Oncology Group (ECOG) Performance Status 0 or 1 * Child Pugh class A * Documented virology status of hepatitis, as confirmed by screening hepatitis B virus (HBV) and hepatitis C virus (HCV) serology tests. * For subjects with active HBV, HBV deoxyribonucleic acid (DNA) \< 500 IU/mL obtained ≤ =\< 28 days prior to randomization, and anti-HBV treatment (per local standard of care; e.g., entecavir) for a minimum of 14 days prior to randomization and willingness to continue treatment for the length of the study * At least one measurable untreated malignant lesion per RECIST v1.1. Subjects who previously received loca…