Sorafenib Tosylate in Treating Patients With Liver Cancer Who Have Undergone a Liver Transplant

Inclusion Criteria: * Patients with HCC on explant, who have not received prior systemic anti-cancer treatment for HCC * HCC patients who have undergone orthotopic liver transplantation, are at high risk for tumor recurrence or who have high suspicion or documentation of tumor recurrence * Patients who have a life expectancy of at least 12 weeks * Patients must have one of the following disease states: * Patients are 4 weeks beyond and less than 60 days from liver transplant surgery (to first study treatment) who have no residual hepatocellular carcinoma following liver transplantation; * Patients with post transplant recurrent hepatocellular carcinoma within the liver or at an extra hepatic site, diagnosed by radiographic imaging (computed tomography \[CT\] or magnetic resonance imaging \[MRI\]) consistent with hepatocellular carcinoma or proved by biopsy, within 24 months of transplantation; * Post-transplant patients with rising alpha-feta protein level \> 500ng/mL, even in the absence of confirmed disease within 24 months of transplant * Patients must have one of the following explant histological features of HCC:bilobar tumor; macrovascular invasion; or multifocality; if patients have well-differentiated HCC, they must have all three features * Patients who have an Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Platelet count \>= 60 x 10\^9/L * Hemoglobin \>= 8.5 g/dL * Total bilirubin =\< 3 mg/dL * Alanine transaminase (ALT) and aspartate transaminase (AST) =\< 5 x upper limit of normal * Amylase and lipase =\< 1.5 x the upper limit of normal * Serum creatinine =\< 1.5 x the upper limit of normal * Prothrombin time (PT)-international normalized ratio (INR) =\< 2.3 or PT 6seconds above control * Patients who give written informed consent Exclusion Criteria: * Previous or concurrent cancer that is distinct in primary site or histology from HCC, EXCEPT cervical carcinoma in situ, treated basal cell carcinoma,superficial bladder tumors (Ta, Tis \& T1); any cancer curatively treated \> 3 years prior to entry is permitted * Renal failure requiring hemo- or peritoneal dialysis * History of cardiac disease: congestive heart failure \> New York Heart Association (NYHA) class 2; active coronary artery disease (CAD); cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers ordigoxin; or uncontrolled hypertension; myocardial infarction more than 6months prior to study entry is permitted * Active clinically serious infections \> grade 2 (National Cancer Institute -Common Terminology Criteria for Adverse Events version 3.0) * Known history of human immunodeficiency virus (HIV) infection * Known central nervous system tumors including metastatic brain disease * Patients with clinically significant gastrointestinal bleeding within 30 days prior to study entry * Substance abuse, medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of the study results * Known or suspected allergy to the investigational agent or any agent given in association with this trial * Patients unable to swallow oral medications * Any condition that is unstable or which could jeopardize the safety of the patient and his/her compliance in the study * Pregnant or breast-feeding patients; women of childbearing potential must have a negative pregnancy test performed within seven days prior to the start of study drug; both men and women enrolled in this trial must use adequate barrier birth control measures during the course of the trial * Prior use of any systemic anti-cancer chemotherapy for HCC * Prior use of systemic investigational agents for HCC * Prior use of Raf-kinase inhibitors (RKI), VEGF inhibitors, MEK inhibitors or Farnesyl transferase inhibitors * Use of biologic response modifiers, such as granulocyte colony-stimulating factor (G-CSF), within 3 weeks prior to study entry (G-CSF and other hematopoietic growth factors may be used in the management of acute toxicity, such as febrile neutropenia, when clinically indicated or at the discretion of the investigator; however, they may not be substituted for a required dose reduction) * Patients taking chronic erythropoietin are permitted provided no dose adjustment is undertaken within 1 month prior to the study or during the study * Autologous bone marrow transplant or stem cell rescue within four months of start of study drug * Concomitant treatment with rifampin and St John's wort * Concomitant anti-coagulation therapy with warfarin