MK2206 in Treating Patients With Advanced Refractory Biliary Cancer That Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have histologically confirmed biliary tract carcinoma that is surgically unresectable * Cytological confirmation is not allowed on this study, as tissue is needed for correlative science analysis * Either fresh-frozen tissue (FFT) or paraffin-embedded tissue blocks (PETB) will be required from patients before enrolling on this study * No biopsies will be required unless there is insufficient tissue or if the PETB available is more than 12 months old * 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 ≥ 10 mm with spiral CT scan (CT scan slice thickness no greater than 5 mm) * Malignant lymph nodes will be considered measurable if they are ≥ 15 mm in short axis * Patients must have received one prior therapy for metastatic disease * No prior Akt inhibitors allowed * Patients with known brain metastases should be excluded from this clinical trial * Life expectancy greater than 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status (PS) =\<2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelet count \>= 100,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\] =\< 2.5 x IULN * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal (measured or calculated using the Cockroft-Gualt formula) * Women of childbearing potential and men 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 * Not pregnant or nursing * Able to swallow oral tablets * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to Akt Inhibitor MK2206 (MK2206) or other agents used in the study * Patients with diabetes or in risk for hyperglycemia should not be excluded from trials with MK2206, but the hyperglycemia should be well controlled on oral agents before the patient enters the trial * Cardiovascular: baseline QTcF \> 450 msec (male) or QTcF \> 470 msec (female) will exclude patients from entry on study * Patients with clinically significant bundle branch block or pre-existing clinically significant bradycardia will be excluded from the study * No 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 * No concurrent grapefruit or grapefruit juice * For patients having prior cryotherapy, radiofrequency ablation, ethanol injection, transarterial chemoembolization (TACE), or photodynamic therapy, the following criteria must be met: * 6 weeks has elapsed since that therapy * Indicator lesion(s) is/are outside the area of prior treatment or, if the only indicator lesion is inside the prior treatment area, there must be clear evidence of disease progression associated with that lesion * Edges of the indicator lesion are clearly distinct on CT scanning * Prior radiation therapy with or without the use of a fluoropyrimidine as a radiosensitizer in the adjuvant setting will be allowed on study if \> 12 weeks have elapsed since therapy * Prior palliative radiation therapy will allowed as long as \> 4 weeks have elapsed since therapy * No patients who have had 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 * Patients may not be receiving any other investigational agents * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients receiving any medications or substances that are inhibitors or inducers of CYP 450 3A4 are ineligible