Cediranib Maleate in Treating Patients With Locally Advanced or Metastatic Liver Cancer

Inclusion Criteria: * Histologically confirmed hepatocellular carcinoma * Locally advanced or metastatic disease * Not amenable to treatment with surgery or orthotopic liver transplantation * Measurable or non-measurable disease * Measurable disease is defined as ≥ 1 unidimensionally measurable lesion ≥ 20 mm by conventional techniques OR ≥ 10 mm by spiral CT scan * Evidence of disease progression by imaging on serial exams or biochemical evidence of a rising alpha fetoprotein on serial testing * No history of brain metastases other than locally treatable CNS lesions (i.e., lesions treatable with surgery or radiosurgery) * Patients with locally treatable CNS disease eligible provided they were previously treated and had no evidence of CNS progression for ≥ 4 weeks after completion of treatment * No fibrolamellar hepatocellular carcinoma or mixed cholangiocarcinoma/hepatocellular carcinoma * Performance status - ECOG 0-1 * Absolute neutrophil count ≥ 1,200/mm\^3 * Platelet count ≥ 75,000/mm\^3 * Hemoglobin ≥ 10.0 g/dL * Bilirubin ≤ 3 times upper limit of normal (ULN) * AST ≤ 5 times ULN * Alkaline phosphatase ≤ 5 times ULN * Urine protein \< 1+ by urine dip stick OR proteinuria \< 1 gm/24-hour collection * QTc prolongation ≤ 500 msec * No symptomatic congestive heart failure * No unstable angina pectoris * No cardiac arrhythmia * No uncontrolled blood pressure, defined as systolic blood pressure \> 150 mm Hg and/or diastolic blood pressure \> 100 mm Hg * No significant ECG abnormality within the past 14 days * No New York Heart Association class III or IV disease * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No other malignancy within the past 5 years except basal cell or squamous cell skin cancer or carcinoma in situ of the cervix * No history of allergic reaction to compounds of similar chemical or biological composition to AZD2171 * No ongoing or active infection * No psychiatric illness or social situation that would preclude study participation * No other uncontrolled illness * More than 4 weeks since prior biologic therapy * More than 4 weeks since prior and no concurrent immunotherapy * No colony-stimulating factors during the first course of study treatment * At least 6 weeks since prior chemoembolization * Patients must have evidence of disease progression or new metastases after prior chemoembolization * No prior systemic chemotherapy for this cancer * No other concurrent chemotherapy * More than 4 weeks since prior hormonal therapy * See Disease Characteristics * At least 6 weeks since prior radiofrequency ablation or other local ablative therapy * Patients must have evidence of disease progression or new metastases after prior radiofrequency ablation or other local ablative therapy * No prior external beam radiotherapy to the primary site * No prior radiotherapy to ≥ 25% of the bone marrow * No concurrent radiotherapy * See Disease Characteristics * No concurrent combination antiretroviral therapy for HIV-positive patients * No concurrent drugs or biologics with proarrhythmic potential