Selumetinib in Treating Patients With Locally Advanced or Metastatic Liver Cancer

Inclusion Criteria: * Meets 1 of the following criteria: * Histologically or cytologically confirmed hepatocellular carcinoma * Serum alpha fetoprotein \> 1000ng/dL with characteristic imaging findings coupled with the appropriate clinical scenario (i.e., chronic hepatitis and/or cirrhosis) * Child's A or B cirrhosis allowed * If Child's B cirrhosis is present, the patient may not have significant encephalopathy or ascites that requires paracentesis and must meet laboratory criteria (i.e., well-compensated Child's B) * Metastatic disease (including any proven lymph node metastases) or localized disease not amenable to potentially curative transplant/locoregional/surgical therapy as determined by a qualified surgeon or tumor board * Measurable disease, defined as at least one unidimensionally measurable ≥ 20 mm by conventional techniques or ≥ 10 mm by spiral CT scan * No known brain metastases * ECOG performance status ≤ 2 * Life expectancy \> 3 months * Leukocytes ≥ 3,000/mm³ * Absolute neutrophil count ≥ 1,500/mm³ * Platelets ≥ 75,000/mm³ * Total bilirubin \< 2 times upper limit of normal (ULN) * AST/ALT \< 5 times ULN * Creatinine \< 1.5 mg/dL or creatinine clearance ≥ 60 mL/min * INR \< 1.4 * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception before, during, and for 4 weeks after completion of study treatment * Willing to undergo protocol-required tumor biopsies (patients must also be able to have any anticoagulation held for an appropriate period of time) * No history of allergic reactions attributed to compounds of similar chemical or biological composition to AZD6244 or its excipient Captisol® * No refractory nausea and vomiting or chronic gastrointestinal diseases (e.g., inflammatory bowel disease) that would preclude adequate absorption * No uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements * No active illicit substance or alcohol abuse * Able to understand and willing to sign a written informed consent document * Recovered from prior therapy * At least 4 weeks since prior chemo embolization, radio embolization (90Y microspheres), resection, or radio frequency/cryoablation * Must have measurable disease outside the treated area or unequivocal evidence of disease progression within the treated area * More than 4 weeks since prior radio therapy or major surgery * No prior organ transplantation * No prior systemic chemotherapy * No prior sorafenib * No prior therapeutic antibody or experimental systemic therapy (oral or intravenous) * No prior hepatic artery infusion of chemotherapy * No prior mitogen-activated protein kinase inhibitor * No prior significant bowel resection that would preclude adequate absorption * No concurrent fruit or juice of the grapefruit during AZD6244 therapy * No concurrent anti retroviral therapy for HIV-positive patients * No other concurrent investigational or commercial agents or therapies for this cancer