Sorafenib and Nivolumab in Treating Participants With Unresectable, Locally Advanced or Metastatic Liver Cancer

PRIMARY OBJECTIVES: I. Maximum tolerated dose (MTD) of sorafenib tosylate (sorafenib) in combination with standard dose nivolumab with Child Pugh A-B7 liver function. (Part 1: Escalation Cohort). II. Safety in participants with Child-Pugh B liver function. (Part 2: Child-Pugh B Escalation Cohort) SECONDARY OBJECTIVES: I. Safety and tolerability of combination overall. (Parts 1 and 2). II. Rate of immune-related adverse event (irAE) for combination overall and in participants with Child-Pugh B liver function. (Parts 1 and 2). III. Overall response rate (ORR) by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 in participants with Child-Pugh B liver function. (Parts 1 and 2). IV. Duration of response (DOR), progression free survival (PFS), and overall survival (OS) for escalation cohort and Child-Pugh B expansion cohort and overall. (Parts 1 and 2). EXPLORATORY OBJECTIVES: I. Relationship between peripheral blood mononuclear cell (PBMC) immune cell subset frequencies, baseline liver function, and clinical outcomes. II. Relationship between PBMC T cell receptor (TCR) clonotype frequency and diversity, baseline liver function, and clinical outcomes. III. Tumor tissue immune cell subsets and TCR clonotype frequency and diversity in pre-treatment archival tumor tissue samples. IV. Tumor and immune cell programmed death-ligand 1 (PD-L1) status in pre-treatment archival tumor tissue samples and relationship to clinical outcomes. V. Changes in hepatitis B virus (HBV) and/or hepatitis C virus (HCV) viral load on treatment. VI. Alpha-fetoprotein (AFP) changes on treatment and relationship to clinical outcomes. VII. Relationship between clinical outcomes and clinicopathologic features including race/ethnicity, etiology of liver disease including HBV/HCV status, baseline liver function, presence of cirrhosis, macrovessel invasion, extrahepatic spread, site(s) of metastatic disease, prior treatment history including prior radiation and arterial therapies. OUTLINE: This is a dose-escalation and expansion study of sorafenib tosylate. DOSE-ESCALATION (Part 1): Between 3-12 participants will be enrolled in Part 1. Participants receive sorafenib tosylate orally (PO) once daily (QD) or twice daily (BID) on days 1-28, and nivolumab intravenously (IV) over 30 minutes on days 1 and 15. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. EXPANSION COHORT (Part 2). Participants receive nivolumab IV over 30 minutes on days 1 and 15, and sorafenib tosylate once daily (QD) or twice daily (BID) on days 1-28. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, participants are followed up at 30 and 100 days, then every 3 months for up to 2 years after the last dose.