Radiation Therapy With Protons or Photons in Treating Patients With Liver Cancer

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 * Patient 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 lesion that is \>= 1 cm and =\< 15 cm in greatest dimension is allowed * Age \>= 18 * 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 \>= 2.5 g/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 REGISTRATION: * 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