The purpose of this study is to find out what effects, good and/or bad, the combination of the drug sorafenib in combination with the drug doxorubicin might have on the growth and spread of liver cancer (HCC).

Inclusion Criteria:

• Diagnosis of HCC confirmed histologically, excluding mixed HCC histology (e.g. HCC plus cholangiocarcinoma) or fibrolamellar variant.
• Prior treatment with sorafenib as single agent or in combination, with no less than 200 mg once every other day dose of sorafenib, with radiologic evidence of progression of disease.
• Measurable disease using RECIST 1.1 criteria.
• Non-cirrhotic or no more than Child-Pugh A cirrhosis.
• Expected survival of at least 3 months.
• Age ≥ 18 years.
• KPS ≥ 70%
• Fully recovered from any prior surgery and/or radiation and none within 2 weeks of initiating treatment.
• Patients may have been treated with locoregional liver directed therapies such as embolization, chemo-embolization including drug-eluting beads doxorubicin chemoembolization (prior non drug eluting beads chemoembolization with doxorubicin is excluded), radiation, radioactive microspheres, etc., provided that they either have a target lesion that has not been subjected to local therapy and/or the target lesion(s) within the field of the local therapy has shown an increase of ≥25% in the size since last treatment. Such therapy must be completed at least 4 weeks prior to treatment initiation. Patients that have received palliative radiation therapy to the bone need not wait 4 weeks to begin protocol therapy.
• Informed consent must be obtained prior to study initiation.
• Total bilirubin ≤3.0 mg/dL and no evidence of bile obstruction.
• Absolute neutrophil count (ANC) ≥1,500/μL.
• Platelets ≥75,000/μL.
• Serum creatinine ≤ 1.5 x the upper limit of normal range, or, if serum creatinine >1.5 x the upper limit of normal range, then the creatinine clearance must be ≥ 60 mL/min.
• Subjects with active hepatitis B or C on anti-viremic compounds may remain on such treatment, except for interferon.
• Patients with a history of hypertension should be well controlled (< 140/90 mmHg) on a regimen of anti-hypertensive therapy.
• Brain metastases are allowed if well controlled and without seizures.
• Prior palliative radiation therapy to bone sites is allowed as long as it is completed more than two weeks ago.

Exclusion Criteria:

• Significant cardiac disease:
• Congestive heart failure > Class II New York Heart Association (NYHA).
• Myocardial infarction within 6 months prior to study entry.
• Cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin.
• Serious myocardial dysfunction, defined as scintigraphically (MUGA, myocardial scintigram) or echocardiogram determined absolute left ventricular ejection fraction (LVEF) below normal (<50%).
• Participation in concurrent investigational studies.
• Prior loco-regional therapy including drug-eluting beads doxorubicin chemoembolization (prior non drug eluting beads chemoembolization with doxorubicin is excluded) is allowed.
• Prior exposure to systemic intravenously given doxorubicin.
• Pregnancy or lactation.
• Uncontrolled inter-current illness or psychiatric illness or social situations that would limit compliance with study requirements.
• Subjects with history of another primary cancer, with the exception of: a) curatively resected non-melanoma skin cancer; b) curatively treated cervical carcinoma in situ; or c) other primary solid tumor with no known active disease present in the opinion of the investigator will not affect patient outcome in the setting of current HCC diagnosis. Allografts, including but not limited to liver and bone marrow transplants.
• Bleeding esophageal or gastric varices within 30 days prior to treatment initiation.

Concomitant treatment with Rifampin or St John's Wort. Patients should discontinue these drugs at least 4 weeks prior to starting protocol treatment.

• Subjects known to be HIV positive.
• History of bleeding diathesis.