Cohorts of 3-6 patients receive escalating doses of oblimersen and doxorubicin until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 3 or 2 of 6 patients experience dose-limiting toxicity. Once the MTD is determined, additional patients*, including 6 patients with hepatocellular carcinoma (HCC), are treated at the recommended phase II dose. (Phase I completed as of 1/16/04.)