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