Dasatinib in Treating Patients With Advanced Liver Cancer That Cannot Be Removed by Surgery

Criteria:

* WBC \>= 3,000/mm\^3
* LVEF normal
* Histologically or cytologically confirmed hepatocellular carcinoma; Advanced disease, unresectable disease, no Childs C criteria
* Measurable disease, defined as \>= 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques or \>= 10 mm by spiral CT scan
* Not a candidate for percutaneous ethanol injection or radiofrequency ablation (RFA)
* Prior transarterial chemoembolization, ethanol, and RFA allowed if new lesions are present in the liver and there are no other sites of disease
* No pleural effusion or ascites requiring paracentesis within the past 4 weeks
* No known brain metastases
* ECOG performance status (PS) 0-1 OR Karnofsky PS 70-100%
* Life expectancy \> 3 months
* Absolute neutrophil count \>= 1,500/mm\^3
* Platelet count \>= 75,000/mm\^3
* Bilirubin =\< 2 times upper limit of normal (ULN)
* AST and ALT =\<2.5 times ULN (5 times ULN if liver involvement by tumor)
* Creatinine =\< 2 times ULN
* PT =\< 1.5 times ULN (no anticoagulation)
* Albumin \>= 2.5 mg/dL
* No history of allergic reactions attributed to compounds of similar chemical or biological composition to dasatinib
* No evidence of encephalopathy
* No condition that would preclude ability to swallow and retain dasatinib tablets, including any of the following:

  * Gastrointestinal tract disease resulting in an inability to take oral medication;
  * Requirement for IV alimentation;
  * Prior surgical procedures affecting absorption:
  * Active peptic ulcer disease
* No clinically significant ECG abnormalities
* No clinically significant cardiovascular disease, including any of the following:

  * Myocardial infarction or ventricular tachyarrhythmia within the past 6 months;
  * Prolonged QTc \>= 480 msec (Fridericia correction);
  * Major conduction abnormality (unless cardiac pacemaker is present)
* No other uncontrolled illness, including, but not limited to, any of the following:

  * Ongoing or active infection;
  * History of significant bleeding disorder, including congenital (von Willebrand's disease) or acquired disorders (antifactor VIII antibodies);
  * Psychiatric illness or social situation that would preclude study compliance
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* Recovered from all prior therapy
* One prior systemic chemotherapy regimen allowed
* Prior cryosurgery allowed
* More than 4 weeks since prior transarterial chemoembolization
* More than 4 weeks since prior radiotherapy
* Prior or concurrent localized palliative radiotherapy (i.e., bony metastasis) allowed provided it was administered for =\< 3 days
* At least 7 days since prior and no concurrent antithrombotic and/or antiplatelet agents (e.g., warfarin, heparin, low molecular weight heparin, acetylsalicylic acid, and/or ibuprofen)
* At least 7 days since prior and no concurrent agents with proarrhythmic potential
* At least 7 days since prior and no concurrent medications or substances that are potent inhibitors or inducers of CYP3A4
* No concurrent combination antiretroviral therapy for HIV-positive patients
* No concurrent embolization or chemoembolization
* No concurrent systemic antacids (H2 receptor antagonists or proton pump inhibitors)
* Locally active antacids allowed provided they are held for 2 hours before and 2 hours after dasatinib dose
* No other concurrent investigational agents
* No other concurrent anticancer agents or therapies