Sorafenib Tosylate and Pembrolizumab in Treating Patients With Advanced or Metastatic Liver Cancer

PRIMARY OBJECTIVES: I. To assess the overall response rate (ORR) related to the combination of sorafenib tosylate (sorafenib) + pembrolizumab in advanced hepatocellular carcinoma patients. SECONDARY OBJECTIVES: I. To assess time to tumor progression in patients who received the combination therapy of sorafenib + pembrolizumab compared to historical data on sorafenib only treatment in patients with advanced hepatocellular carcinoma. TERTIARY OBJECTIVES: I. To obtain data on changes in immune cell function and in the tumor microenvironment pre- and post-treatment to screen for potential biomarkers that may be able to predict clinical benefit. \- All patients will be followed for survival OUTLINE: Patients receive sorafenib tosylate orally (PO) twice daily (BID) on days -28 to -1 and 1-21. Patients also receive pembrolizumab intravenously (IV) over 30 minutes on day 1. Courses repeat every 3 weeks in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up at 30 days, every 3 months for up to 1 year, then every 6 months thereafter.