AZD2171 in Treating Patients With Locally Advanced Unresectable or Metastatic Liver Cancer

Inclusion Criteria: * Histologically or cytologically confirmed hepatocellular carcinoma * Locally advanced unresectable OR metastatic disease * Cancer of the Liver Italian Program (CLIP) score =\< 3 * Symptomatic congestive heart failure * Unstable angina pectoris * Measurable disease, defined as \>= 1 unidimensionally measurable lesion\>= 20 mm by conventional techniques OR \>= 10 mm by spiral CT scan * Cardiac arrhythmia * Measurable lesion must be outside field of prior chemoembolization * No known brain metastases * ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100% * Life expectancy \> 12 weeks * Absolute neutrophil count \>= 1,000/mm\^3 * Platelet count \>= 75,000/mm\^3 * Hemoglobin \>= 8 g/dL * Bilirubin =\< 3.0 mg/dL * AST and ALT =\< 7 times upper limit of normal * Creatinine =\< 2.0 mg/dL * Fertile patients must use effective contraception * CLIP score =\< 3 Exclusion Criteria: * Not pregnant or nursing * Negative pregnancy test * No history of allergic reactions attributed to compounds of similar chemical or biological composition to AZD2171 * No chronic diarrhea or any disorder that would limit adequate absorption of AZD2171 * No familial history of long QT syndrome * Proteinuria =\< +1 on two consecutive dipsticks taken no less than 1 week apart * No other uncontrolled illness including, but not limited to, any of the following: * Hypertension * Ongoing or active infection * No psychiatric illness or social situation that would limit study compliance * Recovered from prior therapy * Prior systemic chemotherapy regimens for hepatocellular carcinoma allowed * More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) * More than 4 weeks since prior radiotherapy, major surgery, or chemoembolization * At least 30 days since prior participation in an investigational trial * No other concurrent investigational agents * No concurrent medication that may markedly affect renal function (e.g., vancomycin, amphotericin, or pentamidine) * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent anticancer agents or therapies * No mean QTc \> 470 msec (with Bazett's correction) on screening EKG (490 msec for women)