Sorafenib Tosylate With or Without Stereotactic Body Radiation Therapy in Treating Patients With Liver Cancer

PRIMARY OBJECTIVES: I. To determine if stereotactic body radiation therapy (SBRT) improves overall survival in hepatocellular carcinoma (HCC) patients treated with sorafenib (sorafenib tosylate). SECONDARY OBJECTIVES: I. To determine the difference in time to progression (TTP) and progression-free survival (PFS) in HCC patients treated with sorafenib compared to SBRT followed by sorafenib. II. To measure differences in toxicity in HCC patients treated with sorafenib versus SBRT followed by sorafenib. III. To measure vascular thrombosis response post sorafenib versus SBRT followed by sorafenib. IV. To measure differences in health related quality of life (QOL) and quality-adjusted survival in HCC patients treated with sorafenib compared to SBRT followed by sorafenib. V. Collection of biospecimens for future correlative studies to investigate differences in potential biomarkers in patients treated with sorafenib versus SBRT followed by sorafenib.