This phase Ib/II trial studies how well sorafenib tosylate and pembrolizumab work in treating patients with liver cancer that has spread to other parts of the body. Sorafenib tosylate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Monoclonal antibodies, such as pembrolizumab, may interfere with the ability of tumor cells to grow and spread. Giving sorafenib tosylate and pembrolizumab may work better in treating patients with 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.

Inclusion Criteria:

• Participant must have histologically or radiographically confirmed hepatocellular cancer (HCC) that is advanced or metastatic and if archival tissue is available, have archival tissue submitted for PD-L1, PD-L2 testing
• Participants with measurable disease that has progressed are eligible if prior surgery or locoregional therapy occurred > 28 days prior to enrollment
• Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 (Karnofsky >= 60%)
• Child-Pugh class-A liver function
• Absolute neutrophil count (ANC) >= 1,500/ mcL
• Hemoglobin >= 8.5 g/dL
• Platelets >= 75,000/ mcL
• Total bilirubin =< 2.0 mg/dL
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 5 X ULN
• Serum Creatinine <= 1.5 upper limit of normal (ULN)or Creatinine clearance > 50 mL/minute if serum creatinine is elevated above 1.5 X ULN
• Have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria present
• Ability to swallow and retain oral medication
• Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately
• Participant must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure
• Participants with past or ongoing hepatitis C virus (HCV) infection will be eligible for the study. The treated participants must have completed their treatment at least 1 month prior to starting study intervention.
• Participants with controlled hepatitis B will be eligible as long as they meet the following criteria:

Antiviral therapy for HBV must be given for at least 12 weeks and HBV viral load must be less than 100 IU/ml prior to first dose of study drug. Participants on active HBV therapy with viral loads under 100 IU/mL should stay on the same therapy throughout study treatment Participants who are anti-HBc , negative for Hepatitis B surface antigen (HBsAg) and negative or positive for anti-HBs, and who have an HBV viral load under 100 IU/mL , do not require HBV anti-viral prophylaxis

Exclusion Criteria:

• One prior line of therapy that may include a PDL1 blocker allowed, no prior sorafenib or PD1 blocker allowed.
• Participants who have had radiotherapy or chemotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier
• Any evidence of bleeding diathesis (patients on therapeutic warfarin or heparin will be excluded)
• Participants with a history of variceal bleed within 6 months prior to enrollment
• Known human immunodeficiency virus (HIV)-positive participants (even if on combination retrovirals, participant will be excluded
• Participants with chronic autoimmune disease
• Participants with known brain metastases should be excluded from this clinical trial
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Has known history of, or any evidence of active, non-infectious pneumonitis
• Pregnant or nursing female participants
• Unwilling or unable to follow protocol requirements
• Any condition which in the Investigator's opinion deems the participant an unsuitable candidate to receive study drug
• Received a live vaccine within 30 days prior to start of study treatment