This pilot clinical trial studies stereotactic body radiation therapy (SBRT) and transarterial chemoembolization (TACE) in treating patients with liver cancer that cannot be removed by surgery. SBRT is a specialized radiation therapy that delivers a high dose of radiation directly to the tumor and may kill more tumor cells and cause less damage to normal tissue. Chemoembolization kills tumor cells by carrying drugs directly into blood vessels near the tumors and then blocking the blood flow to allow a higher concentration of the drug to reach the tumor for a longer period of time. SBRT may make TACE more beneficial by increasing blood flow to the tumor, which may allow more of the TACE chemotherapy to enter the tumor. Giving SBRT with TACE may work better in treating patients with liver cancer that cannot be removed by surgery.