Sorafenib and Vorinostat in Treating Patients With Advanced Liver Cancer

Inclusion Criteria:

* Diagnosis of HCC by biopsy-proven pathologic diagnosis or by clinical criteria as defined below:

  \* Clinical criteria to be met if patient has a history of cirrhosis or chronic hepatitis B infection:
  * Imaging abnormalities \> 1 cm in size with classic enhancement by magnetic resonance imaging (MRI) or triple-phase computed tomography (CT) scan
  * Alpha-fetoprotein (AFP) of any value
* Performance status Eastern Cooperative Oncology Group (ECOG) =\< 1
* If cirrhosis, Child-Pugh classification A or B
* Total bilirubin =\< 3.0 mg/dL
* Creatinine =\< 1.5 x upper limit of normal for the laboratory
* International normalized ratio (INR) =\< 1.7 (if not due to anticoagulants)
* Absolute neutrophil count (ANC) \>= 1,500/mm\^3
* Platelets \>= 80,000/mm\^3
* Hemoglobin (Hgb) \>= 8.5 g/dL (transfusion or erythropoietin-like substances not permitted prior to baseline evaluation)
* Any prior therapies such as surgery, chemoembolization, radiofrequency ablation, and alcohol injection are allowed as long as toxicity from such prior therapy is =\< grade 1
* Prior sorafenib is allowed as long as toxicity from ongoing is ≤ grade 2 and prior intolerance of 400 mg sorafenib PO daily is felt amenable, by the principal investigator, to supportive care measures or dose modifications.
* Measurable or evaluable disease by Response Evaluation Criteria in Solid Tumors (RECIST) criteria version (v) 1.1 mRECIST or elevated AFP
* Ability to understand and willingness to sign a written informed consent; a signed informed consent must be obtained prior to any study specific procedures
* Women of childbearing potential must have a negative pregnancy test performed within 2 weeks prior to the start of treatment
* Women of childbearing potential and men must agree to use a medically accepted form of birth control for the duration of study participation and for 4 months following completion of study treatment

Exclusion Criteria:

* Candidate for curative therapy including surgical resection or orthotopic liver transplantation
* Known central nervous system metastasis
* Any investigational agent within 4 weeks of first dose of study treatment
* Known intolerance of vorinostat
* Unable to swallow medication
* Unable to swallow medication; suspected malabsorption
* Active alcohol abuse
* Contraindication to antiangiogenic agents, including:

  * Pulmonary hemorrhage/bleeding event \>= grade 2 within 4 weeks of first dose of study drug
  * Any other hemorrhage/bleeding event \>= grade 3 within 4 weeks of first dose of study treatment
  * Serious non-healing wound, ulcer, or bone fracture
* Thrombolic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months; hepatic portal vein thrombus is not considered an exclusion criterion
* Major cardiac dysfunction, such as uncontrolled angina, congestive heart failure with New York Heart Association (NYHA) class III or higher, known left ventricular ejection fraction less than 40%
* Systolic blood pressure \> 160 mmHg or diastolic pressure \> 90 mmHg despite optimal medical management
* Significant lung disease (oxygen \[O2\] saturation less than 88% in room air)
* Serious uncontrolled infection; known human immunodeficiency virus (HIV)-seropositivity requiring retroviral therapy, or diagnosis of acquired immune deficiency syndrome (AIDS); diagnosis of chronic hepatitis B or C allowed
* Medical, psychological, or social conditions that, in the opinion of the investigator, may increase the patient's risk or interfere with the patient's participation in the study or hinder evaluation of the study results