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

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/In…