Inclusion Criteria:

• * Pathologically (histologically or cytologically) or radiographically-proven (based on the American Association for the Study of Liver Diseases \[AALSD\] criteria) unresectable or locally recurrent hepatocellular cancer prior to registration
• * Appropriate stage for study entry based on the following diagnostic workup:
• * All patients must have computed tomography (CT) scan chest/abdomen/pelvis with multiphasic liver CT scan prior to registration. If CT contrast is contraindicated, CT chest without contrast and magnetic resonance imaging (MRI) of abdomen is permitted
• * Participants must have measurable disease at study entry, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 2 cm with conventional techniques or as \> 1 cm with spiral CT scan
• * Patients must have 3 or fewer single or multinodular tumors. For patients with a single lesion, lesion must be 15 cm or less in greatest dimension. For patients with two lesions, no lesion may be greater than 10 cm in greatest dimension. For patients with three lesions, no lesion may be greater than 6 cm in greatest dimension. Portal vein involvement or thrombosis combined with a single legion that is ≥ 1 cm and ≤ 15 cm in greatest dimension is allowed.
• * Zubrod performance status 0-1 within 30 days prior to registration
• * Negative urine or serum pregnancy test for women of childbearing potential within 7 days prior to study entry
• * Absolute neutrophil count (ANC) \>= 1,000 cells/mm\^3
• * Platelets \>= 50,000 cells/mm\^3
• * Hemoglobin \>= 9.0 g/dl; (Note: The use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 9.0 g/dl is acceptable)
• * Total bilirubin \< 4 x institutional upper limit of normal (ULN)
• * Transaminases (aspartate aminotransferase \[AST\] and alanine aminotransferase \[ALT\]) \< 6 x institutional ULN
• * Albumin \>= 2.5mg/dl
• * Creatinine \< 2 mg/dl
• * Prior chemotherapy, targeted biological therapy (e.g. sorafenib), surgery, transarterial chemoembolization (TACE), ablation for present disease is acceptable
• * Must have Child-Turcotte-Pugh (CTP) A or B7
• * The patient or a legally authorized representative must provide study-specific informed consent prior to study registration

Exclusion Criteria:

• * PRIOR TO STEP ONE RANDOMIZATION:
• * Definitive clinical or radiologic documentation of extrahepatic tumor, defined as extrahepatic metastases or malignant nodes (that enhance with typical features of HCC) \> 3.0 cm, in sum of maximal diameters (e.g. presence of one 3.4 cm metastatic lymph node or two 2 cm lung lesions). Note that benign non-enhancing periportal lymphadenopathy is not unusual in the presence of hepatitis and is permitted, even if the sum of enlarged nodes is \> 2.0 cm
• * Uncontrolled prior invasive malignancy, excluding the current diagnosis
• * Systemic chemotherapy for the study cancer \< 2 weeks prior to registration
• * Pregnancy or women of childbearing potential and men who are sexually active and not willing/able to use medically acceptable forms of contraception. This exclusion is necessary because the treatment involved in this study may be significantly teratogenic.
• * HIV positive with CD4 count \< 200 cells/microliter; note that patients who are human immunodeficiency virus (HIV) positive are eligible, provided they are under treatment with highly active antiretroviral therapy (HAART) and have a CD4 count \>= 200 cells/microliter prior to registration. Note also that HIV testing is not required for eligibility for this protocol. This exclusion criterion is necessary because the treatments involved in this protocol may be significantly immunosuppressive.
• * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields (to include Y90)
• * Prior liver transplant
• * PRIOR TO STEP TWO RANDOMIZATION:
• * Unable to obtain confirmation of payment coverage (insurance or other) for either possible treatment