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