TACE With or Without Radiation Therapy in Treating Patients With Stage A-C Liver Cancer

Inclusion Criteria: * HCC is staged as Barcelona A to C * Treatment with SBRT can occur within 6 weeks of registration * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Patient has * Radiographic enhancing liver lesions with early wash out on triple phase CT or MRI or * Histological confirmation of HCC as determined by the Liver Tumor Board * Hemoglobin greater than 10.0 g/dL * Total bilirubin less than 3.0 mg/dL * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 3 X institutional upper limit of normal * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 X institutional upper limit of normal * Total aggregate of maximal dimension of liver tumors is =\< 8 cm * Cirrhotic patients Child Pugh class A or B (score =\< 7) * Patient must be determined by the treating physician to be medically eligible for liver transplantation measured by imaging modality (magnetic resonance imaging \[MRI\]/computed tomography \[CT\] scan) three months post final treatment * Absolute neutrophil count \>= 1,500/μl * Platelet count \>= 50,000 μl (after transfusion if required) * Life expectancy \> 12 weeks * Subjects must have the ability to understand and be willing to provide written informed consent * Women of child-bearing potential must have a negative pregnancy test within 4 weeks to the start of the SBRT treatment * Women must not be pregnant or nursing * Sexually active women must agree to use accepted forms of birth control; acceptable options for birth control will be documented in the consent and discussed with the subject prior to enrollment Exclusion Criteria: * Patient with previous history of abdominal radiation * Cirrhotic patients Child Pugh class B with score \>= 8 * Prior invasive malignancy other than primary liver malignancy (except non-melanomatous skin cancer) unless disease free for a minimum of 3 years * Evidence of metastatic disease prior to registration * Evidence of main portal vein thrombosis * History of known cardiac ischemia or stroke within last 6 months * Any concurrent medical or psychosocial condition that prohibits a major surgical procedure or immunosuppression that would constitute a contraindication to liver transplantation