Floxuridine and Dexamethasone as a Hepatic Arterial Infusion and Bevacizumab in Treating Patients With Primary Liver Cancer That Cannot be Removed by Surgery

DISEASE CHARACTERISTICS: * Histologically confirmed hepatocellular carcinoma (HCC) or intrahepatic cholangiocarcinoma (ICC) * Peripheral, cholangiolar, or cholangiocellular types * Mixed HCC/ICC disease allowed * Unresectable disease * Less than 70% liver involvement * Radiographically bidimensionally measurable disease, defined as lesion ≥ 2 cm in the greatest diameter * May have failed prior systemic chemotherapy or ablative therapy * No radiographic evidence of esophageal varices * No history of variceal hemorrhage * No occlusion of the main portal vein or the right and left portal branches * No clinical ascites * Patients ineligible for first-line MSKCC protocols for HCC are eligible for this study provided there is no clinical or radiographic evidence of extrahepatic disease * No metastatic disease, including CNS metastases PATIENT CHARACTERISTICS: * Life expectancy ≥ 12 weeks * Karnofsky performance status 60-100% * Considered a candidate for general anesthesia and hepatic artery pump placement * Platelet count \> 100,000/mm³ * Albumin \> 2.5 g/dL * Bilirubin \< 1.8 mg/dL * WBC \> 3,500/mm³ * PTT \< 1.5 times upper limit of normal * INR \< 1.5 OR in-range INR (usually 2.0-3.0) for patients on a stable dose of therapeutic warfarin * Urine protein \< 1+ by dipstick or urine analysis OR urine protein:creatinine ratio \< 1.0 * If proteinuria ≥ 2+ at baseline, patient must have \< 1 g protein/24-hour collection * No concurrent disease or illness that would preclude study participation, including any of the following: * Hepatic encephalopathy * Sclerosing cholangitis * Gilbert's disease * Active infection * No known CNS disease * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to bevacizumab * No psychiatric illness or social situation that would preclude study compliance * No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 6 months * No serious or nonhealing active wound, ulcer, or bone fracture * No bleeding diathesis or coagulopathy * No clinically significant cardiovascular disease, including any of the following: * Uncontrolled hypertension, defined as systolic blood pressure (BP) \> 150 mm Hg or diastolic BP \> 100 mm Hg on antihypertensive medications * New York Heart Association class II-IV congestive heart failure * Vascular disease (e.g., aortic aneurysm, aortic dissection) * Myocardial infarction within the past 6 months * Symptomatic peripheral vascular disease * Unstable angina within the past 6 months * History of hypertensive crisis * Transient ischemic attack * Stroke * No other concurrent malignancy except localized basal cell or squamous cell skin cancer * Chronic hepatitis and/or cirrhosis allowed provided it is Child-Pugh class A disease * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception PRIOR CONCURRENT THERAPY: * See Disease Characteristics * More than 4 weeks since prior and no other concurrent experimental therapy except on a Genentech-sponsored bevacizumab cancer study * More than 4 weeks since prior major surgical procedure or open biopsy * More than 1 week since prior minor surgical procedure (e.g., core biopsy), excluding placement of a vascular access device * No prior external-beam radiation therapy to the liver * No prior floxuridine * No chronic daily treatment with nonsteroidal anti-inflammatory medications known to inhibit platelet function * No chronic daily treatment with aspirin (\> 325 mg/day) * No concurrent or recent use of a thrombolytic agent * No concurrent major surgery