Futibatinib and Pembrolizumab for Treatment of Advanced or Metastatic FGF19 Positive BCLC Stage A, B, or C Liver Cancer

Inclusion Criteria: * Age \>= 18 years * Adequate tissue for FGF19 testing by ribonucleic acid (mRNA) or immunohistochemistry (IHC) * Disease characteristics: * Radiologically or pathologically confirmed hepatocellular carcinoma (HCC) that is not eligible for curative resection, transplantation, or ablative therapies * NOTE: Prior radiation, chemoembolization, radioembolization, or other local ablative therapies or hepatic resection are permitted * Measurable disease by any imaging modality as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria in at least one site not previously treated with radiation or liver directed therapy (including bland, chemo- or radio-embolization, or ablation) * NOTE: Tumor lesions in a previously irradiated area are not considered measurable disease; disease that is measurable by physical examination only is not eligible * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (=\< 15 days prior to registration) * Hemoglobin \>= 8.0 g/dL (=\< 15 days prior to registration) * Platelet count \>= 75,000/mm\^3 (=\< 15 days prior to registration) * Albumin \>= 2.5 g/dL (=\< 15 days prior to registration) * Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 2.5 x upper limit of normal (ULN) (or =\< 5 x ULN for patients with liver metastasis) (=\< 15 days prior to registration) * Total bilirubin =\< 2 x ULN (=\< 15 days prior to regis…