Sorafenib Tosylate Following a Liver Transplant in Treating Patients With Liver Cancer

Inclusion Criteria: * Patients must have hepatocellular carcinoma (HCC) with one of the following on explant: microvascular/macrovascular invasion, tumor outside of Milan criteria, poor tumor differentiation; patients with macrovascular invasion on explant pathology will be stratified \* Additionally, the following will be included \*\* Patients with elevated surrogate markers (AFP \> 500 or PIVKA \> 400) pre transplant and with biopsy proven HCC prior to orthotopic liver transplantation (OLT) or on explant * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2 * Patients with a life expectancy \> 12 weeks * Patients must have completed prednisone taper within 6 weeks post OLT * Patients must be enrolled between 6 to 12 weeks post OLT * Cadaveric donors only (no living donor liver transplantation \[LDLT\] or donor after cardiac death transplantation \[DCDT\]) * No sorafenib prior to inclusion in the study * Platelet count \> 50 x 10\^9/L * Hemoglobin \>= 8.5 g/dL * Total bilirubin =\< 5 mg/dL * Alanine transaminase (ALT) and aspartate aminotransferase (AST) =\< 5 x upper limit of normal * Amylase and lipase =\< 1.5 x the upper limit of normal * Serum creatinine \< 2 x the upper limit of normal * Prothrombin time (PT) =\< 6 seconds or international normalized ratio (INR) =\< 2.3 * AFP \> 500 (pre-transplant) * PIVKA \> 400 (pre-transplant) * Patient has not received prior anti-angiogenic therapy, systemic targeted agents or systemic chemotherapy \* P…