Sorafenib Tosylate and Chemoembolization in Treating Patients With Unresectable Liver Cancer

Inclusion * Histologically confirmed hepatocellular carcinoma * AND/OR Magnetic Resonance Imaging (MRI) or Computerized Tomography (CT) consistent with liver cirrhosis AND at least one solid liver lesion \> 2cm with arterial-phase enhancement and delayed washout regardless of alpha-feto protein levels (AFP) * AND/OR AFP \> 400ng/mL AND evidence of at least one solid liver lesion \> 2cm regardless of specific imaging characteristics on CT or MRI * Patient is not a candidate for transplantation, resection, or ablation; for whom the intended therapy is chemoembolization * Patient meets clinical criteria for treatment with chemoembolization * Absolute contraindications to chemoembolization include an uncorrectable bleeding disorder, uncorrectable contrast sensitivity, leukopenia (white blood cell count \< 1000/uL), cardiac or renal insufficiency (serum creatinine \> 2.0mg/dL), hepatic encephalopathy, jaundice, or dilated intrahepatic bile ducts * Portal vein occlusion is a relative contraindication and chemoembolization can be performed only if there are collateral vessels with hepato-pedal flow demonstrated angiographically * Hepatic compromise as determined by the following combination of parameters is a contraindication to therapy: lactate dehydrogenase \> 425 U/L, aspartate aminotransferase \> 100 U/L, total bilirubin \> 2.0 mg/dL and \> 50% liver volume replaced by tumor * Patients may have been treated with ablation or resection in the past, but no sooner than 4 weeks before study registration * Patients may NOT have been previously treated with sorafenib, chemoembolization, radioembolization, or systemic chemotherapy with cytotoxic agents or molecularly targeted agents * ECOG performance status =\< 2 * Life expectancy of greater than 3 months * Platelets \>= 50,000/mcL * Total bilirubin =\< 2.0 mg/dl * AST(SGOT)/ALT(SGPT) =\< 3X institutional upper limit of normal * Creatinine =\< 1.5 mg/dl * INR =\< 1.5 * Patients must have no clinical signs of heart failure and meet New York Heart Association functional classification I or II defined as: Class I - Patients with no limitation of activities; they suffer no symptoms from ordinary activities; Class II - Patients with slight, mild limitation of activity; they are comfortable with rest or with mild exertion * Because agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation * Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion * Patients may not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to sorafenib * History of radiologic contrast reactions not controlled by standard premedications * Patients must not be taking cytochrome P450 enzyme inducing drugs * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, uncontrolled hypertension, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study * Breastfeeding should be discontinued * Prophylactic use of G-CSF or GM-CSF is not permitted on this trial