Thalidomide Plus Interferon Alfa in Treating Patients With Progressive Liver Cancer That Cannot be Surgically Removed

DISEASE CHARACTERISTICS: * Histologically confirmed hepatocellular carcinoma OR * Diagnosis of hepatocellular carcinoma based on characteristic mass and alpha-fetoprotein greater than 500 in the setting of known cirrhosis or chronic hepatitis B or C * Measurable disease * At least 20 mm in one dimension * Not amenable to curative surgical resection PATIENT CHARACTERISTICS: Age: * 18 and over Performance status: * ECOG 0-2 Hematopoietic: * Absolute neutrophil count greater than 1,200/mm\^3 * Hemoglobin at least 8.0 mg/dL * Platelet count at least 25,000/mm\^3 Hepatic: * Bilirubin no greater than 5 mg/dL * Liver function tests no greater than 5 times normal Renal: * Creatinine no greater than 1.5 mg/dL Other: * Not pregnant or nursing * Negative pregnancy test * Regardless of fertility status: * All women (unless they have undergone hysterectomy or have been amenorrheic or postmenopausal for at least 2 years) must use at least 1 highly active method of contraception AND 1 additional effective method of contraception at least 4 weeks before, during, and for at least 4 weeks after study * All men (even if they have undergone a successful vasectomy) must use effective barrier contraception during and for at least 4 weeks after study * No other medical condition that would preclude study * No other prior malignancy in past 5 years except curatively resected basal cell carcinoma of the skin or carcinoma in situ of the cervix PRIOR CONCURRENT THERAPY: Biologic therapy: * No more than 1 prior biologic therapy regimen * No prior interferon or thalidomide for hepatocellular cancer Chemotherapy: * No more than 1 prior chemotherapy regimen Other: * No concurrent barbiturates or alcohol