MK2206 in Treating Patients With Advanced Liver Cancer That Did Not Respond to Previous Therapy

Inclusion Criteria: * Unresectable or metastatic HCC for which standard curative measures do not exist * The diagnosis of hepatocellular carcinoma should be based on at least one of the following: * The presence of one or more liver lesions, measuring \>= 2 cm, with characteristic arterial enhancement and venous washout in the setting of liver cirrhosis and/or hepatitis B or C infection * The presence of liver lesion(s) with AFP \>= 400 * Tissue confirmation in the absence of either or both of the above * Tissue availability is desired and will be sought, but tissue availability is not mandated for accrual to the study * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension, and that has not been the target of local or regional therapy including transarterial chemoembolization, intra-arterial chemotherapy, ethanol, or RFA ablation * One prior line of systemic anti-angiogenic therapy is required; this type of therapy includes, but is not restricted to, sorafenib, bevacizumab, sunitinib, or brivanib given as single agents or in combination with other agents * No clinically evident ascites (minimal, medically controlled ascites detectable on imaging studies only is allowed) * No Child-Pugh C cirrhosis or Child-Pugh B cirrhosis with more than 7 points * No fibrolamellar carcinoma or any mixed variants of HCC with dominant fibrolamellar histology * Patients with known brain metastases should be excluded from this clinical trial * ECOG 0-1 * Life expectancy of greater than 3 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \> 1,000 mcL * Platelets \>= 70,000/mcL * Total bilirubin =\< 1.5 institutional upper limit of normal * AST (SGOT)/ALT (SGPT) \< 5 x institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min * Serum albumin \>= 2.8 g/dL * Not pregnant or nursing * Fertile patients must use two forms of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation * Must agree to collection of correlative blood samples during the study * No patients unable to swallow pills or diagnosed with a gastrointestinal disorder that is likely to interfere with the absorption of MK-2206 or with the patient's ability to take regular oral medication * Patients with hyperglycemia should be well controlled on oral agents before the patient enters the trial * Patients with HgbA1C levels \>= 8% or fasting blood glucose \>= 150 mg/dL are not eligible for this study * Baseline QTcF \> 450 msec (male) or QTcF\> 470 msec (female) will exclude patients from entry on study * Patients with hepatitis B infection, defined by a positive hepatitis B surface antigen test, should be on suppressive anti-viral therapy * Only the following anti-viral therapies are allowed while a patient is on study: tenofovir disoproxil fumarate and entecavir * Patients with hypothyroidism must be on a stable dose of thyroid replacement and be clinically euthyroid * No esophageal or gastric variceal bleeding within the last 6 months * Patients with prior history of variceal bleeding must have had an upper endoscopy (EGD) with appropriate treatment of varices within 6 months prior to study entry * No uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness/social situations that would limit compliance with study requirements * None of the following: * Uncontrolled hypertension (systolic BP \> 150 or diastolic BP \> 100 on two occasions within two weeks of beginning therapy on this protocol) * Myocardial infarction within 6 months * NYHA class \> II * Clinically significant bradycardia related to underlying cardiac disease * Clinically significant bundle branch block related to underlying cardiac disease * No patients with second primary cancer (except adequately treated nonmelanoma skin cancer, curatively treated in-situ cancer of the cervix, or other solid tumors including lymphomas without bone marrow involvement curatively treated with no evidence of disease for ≥ 5 years) * The exception to this criterion is prostate cancer treated definitively with surgery and/or radiation with normal PSA and no clinical evidence of residual or recurrent prostate cancer * HIV-positive patients on combination antiretroviral therapy are ineligible * No history of allergic reactions attributed to compounds of similar chemical orbiologic composition to MK-2206 or other agents used in the study * No medications that cause QTc interval prolongation * Any number of prior regional therapies with transarterial chemoembolization, intra-arterial chemotherapy, or ablative therapy is allowed * No more than 1 prior line of systemic therapy for advanced and/or unresectable disease * No patients who have had anti-angiogenic therapy, chemotherapy, radiotherapy or regional therapy (such as transarterial chemoembolization, intra-arterial chemotherapy) within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Localized radiation for palliation (i.e., bony metastasis, etc.) given for \< 3 days is allowed before therapy and is not subject to the 4-week waiting requirement * Local ablative therapy such as radiofrequency ablation or cryotherapy must have been completed more than 2 weeks prior to study entry * Patients may not be receiving any other investigational or non-investigational agents or therapies directed at treating their hepatocellular carcinoma * Patients may not be receiving any other investigational agents for any condition * Patients receiving any medications or substances that are inhibitors or inducers of CYP3A4 are ineligible