Sorafenib Tosylate and Yttrium Y 90 Glass Microspheres in Treating Patients With Liver Cancer That Cannot Be Removed by Surgery

Inclusion Criteria: * Subjects must be able to understand and be willing to sign the written informed consent form; a signed informed consent form must be appropriately obtained prior to the conduct of any trial-specific procedure * Life expectancy of at least 12 weeks (3 months) * Patients with histological or cytologically documented hepatocellular carcinoma (HCC) (documentation of original biopsy for diagnosis is acceptable if tumor tissue is unavailable) or clinical diagnosis by American Association for the Study of Liver Diseases (AASLD) criteria in cirrhotic subjects is required; for subjects without cirrhosis histological confirmation is mandatory * Patients must have at least one tumor lesion that meets the following criteria: the lesion can be accurately measured in at least one dimension according to Response Evaluation Criteria in Solid Tumor (RECIST) * The target lesion(s) has not been previously treated with local therapy (such as surgery, radiation therapy, hepatic arterial therapy, chemoembolization, radiofrequency ablation, percutaneous ethanol injection or cryoablation) * Patients who have received local therapy, such as surgery, radiation therapy, hepatic arterial embolization, chemoembolization, radiofrequency ablation, percutaneous ethanol injection or cryoablation are eligible if the previously treated lesions have progressed or recurred can be identified as target lesions; local therapy must have been completed at least 4 weeks prior to the baseline scan * Patients who have received yttrium-90 microspheres are not eligible * Patients who have an Eastern Cooperative Oncology Group (ECOG) performance status (PS) =\< 1 * Patients who are categorized under Barcelona-Clınic Liver Cancer (BCLC)-C stage * Cirrhosis grade of Child-Pugh class A; Child-Pugh status should be calculated based on clinical findings and laboratory results during the screening period * Platelet count \>= 60 x 10\^9/L * Hemoglobin \>= 8.5 g/dL * Total bilirubin =\< 2.5 mg/dl * Alanine transaminase (ALT) and aspartate aminotransferase (AST) =\< 5 x upper limit of normal * Serum creatinine =\< 1.5 x the upper limit of normal * Prothrombin time (PT)-international normalized ratio (INR) =\< 2.3 or PT =\< 6 seconds above control * All acute toxic effects of any prior treatment have resolved to National Cancer Institute-Common Terminology Criteria for Adverse Events (NCI-CTCAE) v4.0 grade 1 or less at the time of signing the informed consent form (ICF) * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of study drug; post-menopausal women (defined as no menses for at least 1 year) and surgically sterilized women are not required to undergo a pregnancy test * Subjects (men and women) of childbearing potential must agree to use adequate contraception beginning at the signing of the ICF until at least 30 days after the last dose of study drug; the definition of adequate contraception will be based on the judgment of the principal investigator or a designated associate * Subject must be able to swallow and retain oral medication Exclusion Criteria: * Main portal vein thrombosis (PVT) * Patients who are eligible for curative treatment (ablation or resection or transplantation) * Previous or concurrent cancer other than HCC unless without evidence of disease for 5 or more years prior to entry, except cervical cancer in-situ, treated basal cell carcinoma, or superficial bladder tumor * Tumor replacement \> 70% of total liver volume based on visual estimation by the investigator OR tumor replacement \> 50% of total liver volume in the presence of albumin \< 3 mg/dL * Contraindications to angiography and selective visceral arterial catheterization * Any known contraindications to sorafenib including allergic reaction, pill-swallowing difficulty, uncontrolled hypertension or history of cardiac disease, significant gastrointestinal (GI) bleed within 30 days, metastatic brain disease, renal failure requiring dialysis * Concomitant treatment or within 28 days of one of the following: * Any other systemic anticancer agent other than agents used for cancer prevention * Subjects who have used strong cytochrome P450 3A4 (CYP3A4) inducers (e.g., phenytoin, carbamazepine, phenobarbital, St. John's Wort \[hypericum perforatum\], dexamethasone at a dose of greater than 16 mg daily, or rifampin \[rifampicin\], and/or rifabutin) within 28 days before treatment * UDP glycosyltransferase 1 family, polypeptide A1 (UGT 1A1) and UDP glycosyltransferase 1 family, polypeptide A9 (UGT 1A9) substrates (e.g., irinotecan) * P-glycoprotein (Gp) substrates (e.g., Digoxin) * Prior radiation therapy to the liver * Prior systemic therapy for the treatment of HCC, including sorafenib * Any history of symptomatic pulmonary compromise, such as chronic obstructive pulmonary disease * Any prior intervention for, or ongoing compromise of, the ampulla of Vater or biliary-enteric anastomosis * Clinically evident ascites (trace ascites on imaging is acceptable) * Pregnant or breast-feeding patients * A positive serum pregnancy test within 14 days prior to treatment in women of childbearing potential * Uncontrolled hypertension (systolic pressure \> 140 mm Hg or diastolic pressure \> 90 mm Hg \[NCI-CTCAE v4.0\] on repeated measurement) despite optimal medical management * Active or clinically significant cardiac disease including: * Congestive heart failure-New York Heart Association (NYHA) \> class II * Active coronary artery disease * Cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin * Unstable angina (anginal symptoms at rest), new-onset angina within 3 months before treatment, or myocardial infarction within 6 months before treatment * Evidence or history of bleeding diathesis or uncontrolled coagulopathy * Subject with any pulmonary hemorrhage/bleeding event of NCI-CTCAE v4.0 grade 2 or higher within 4 weeks before treatment; any other hemorrhage/bleeding event of NCI-CTCAE v4.0 grade 3 or higher within 4 weeks before treatment * Subjects with thrombotic, embolic, venous, or arterial events, such as cerebrovascular accident (including transient ischemic attacks) within 6 months of informed consent * Presence of a non-healing wound, non-healing ulcer, or bone fracture * History of organ allograft. (Including corneal transplant) * Known or suspected allergy or hypersensitivity to any of the study drugs, study drug classes, or excipients of the formulations given during the course of this trial * Any malabsorption condition * Inability to comply with the protocol and/or not willing or not available for follow-up assessments