Gefitinib in Treating Patients With Advanced Unresectable Hepatocellular Carcinoma (Liver Cancer)

Inclusion Criteria: * Patients must have advanced unresectable hepatocellular carcinoma based on the following criteria: * Histologically or cytologically confirmed, OR * Alpha-fetoprotein \> 400 ng if patient is not hepatitis surface antigen positive, OR * Alpha-fetoprotein \> 4000 ng if patient is hepatitis surface antigen positive * NOTE: If available, tissue should be submitted to assess EGFR/pathway expression * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral CT scan, assessed within 4 weeks prior to randomization/registration * Prior use of liver-directed therapy (radio-frequency ablation, cryoablation, percutaneous ethanol injection, chemo-embolization, hepatic artery embolization and hepatic artery infused FUDR) is allowed, provided the patient has either progressive hepatic disease or measurable extrahepatic disease * ECOG performance status of 0, 1 or 2 * Leukocytes \>= 2,000/uL OR * Absolute neutrophil count \>= 1,000/uL * Platelets \>= 50,000/uL * Patients may not have Child Pugh Scale's class C cirrhosis * AST (SGOT) =\< 5 x institutional upper limit of normal * Total bilirubin =\< 2 x institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min for patients with creatinine levels above institutional normal * PT =\< 6 seconds over control * INR =\< 2.3 * Albumin \>= 2.8 g/dL * Pregnant women are excluded from this study; sexually active women of child bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control) for the duration of their participation in the study; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Women who are breastfeeding a child are not eligible, unless they discontinue the breastfeeding * Patients must not have had prior systemic chemotherapy, biologic therapy or antiangiogenesis therapy; prior therapy with interferon alpha or interferon beta for treatment of hepatitis B or C is allowed provided * Prior palliative radiotherapy is permissible provided it has been completed 2 weeks from registration and the patient has measurable disease outside the radiation field * Patients may not be receiving any other investigational agents * Patients must not have a history of other malignancies that are active and require therapy (other than local therapies for non melanoma skin cancers) * Patients must not have known brain metastases; their poor prognosis would present challenges and their tendency to develop progressive neurologic dysfunction would confound the evaluation of neurologic and other adverse events * Patients must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to ZD1839 * Patients must not have had prior treatment with an EGFR inhibitor * Patients must not have a history of an uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients must not be HIV-positive and receiving combination anti-retroviral therapy; this therapy might have possible pharmacokinetic interactions with ZD1839; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated * Patients must not use the following known inducers of CYP3A4: carbamazepine, dexamethasone, ethosuxamide, glucocorticoids, griseofulvin, nafcillin, nelfinavir nevirapine, oxcarbazepine, phenobarbital, phenylbutazone, phenytoin, primidone, progesterone, rifabutin, rifampin, rofecoxib, St John's Wort, sulfadimidine, sulfinpyrazone, troglitazone, efavirenz, modafinil, and rifapentine; drugs that induce CYP3A4 enzymes can cause reductions in ZD1839 plasma concentrations below levels thought to be biologically active * Patients must not be candidates for surgical resection or liver transplantation * Patients must not have grade 3 or grade 4 encephalopathy