Eligibility Criteria:
Inclusion Criteria:
* Histologically or cytologically confirmed non-keratinizing nasopharyngeal carcinoma that has recurred at locoregional and/or distant sites, and is not amenable to potentially curative radiotherapy or surgery
* Measurable disease according to the RECIST criteria
* Progressed =\< 24 months of receiving one or two prior line(s) of chemotherapy for recurrent disease, of which at least one line must contain platinum drugs such as cisplatin, carboplatin or oxaliplatin
* ECOG performance status 0, 1, or 2
* Hemoglobin \>= 9 g/dL
* ANC \>= 1,500/μL
* Platelet count \>= 100,000/μL
* Total bilirubin =\< 2.5 times upper limit of normal (ULN)
* ALT =\< 2.5 times ULN (=\< 5 times ULN for patients with liver metastases)
* Creatinine =\< 1.5 times ULN OR creatinine clearance \>= 60 mL/min/1.73 m\^2
* Ability to understand and the willingness to sign a written informed consent document
* Willingness to donate blood for mandatory correlative research studies
* Negative (serum) pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only
Exclusion Criteria:
* Any of the following
* Chemotherapy =\< 4 weeks prior to registration
* Radiotherapy =\< 4 weeks prior to registration
* Nitrosoureas or Mitomycin C =\< 4 weeks prior to registration
* Those who have not recovered from adverse events due to agents administered more than 4 weeks earlier
* NOTE: Prior palliative radiotherapy to bone metastases is allowed =\< 4 weeks prior to registration
* Prior investigational agents =\< 4 weeks prior to registration
* Symptomatic brain metastases; NOTE: primary nasopharyngeal cancers that directly invade the skull base and extend into the infratemporal fossa(e) are not regarded as brain metastases and are not excluded
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to MK-2206 or other agents used in the study
* Prior potent and moderate inhibitors and inducers of CYP3A4 =\< 2 weeks prior to registration:
* Drugs that are forbidden, potent inducers of CYP3A4: phenytoin, phenobarbitone, carbamazepine, barbiturate, rifampicin, St John's Wort.
* Drugs that significantly affect metabolizing activity by way of enzyme inhibition of CYP3A4: ketoconazole, itraconazole, fluconazole, indinavir, ritonavir, erythromycin, cimetidine, clarithromycin
* Unwillingness to go off other inducers and inhibitors of CYP3A4 during the first 2 cycles of MK-2206; NOTE: avoiding these drugs is critical during the first 2 cycles of MK-2206when blood samples are being taken for the correlative study unless there is an urgent medical need and alternatives are not available
* Poorly controlled diabetes mellitus or insulin controlled diabetes; NOTE: As a general guide, patients with a fasting glucose level \> 150 mg/dL (HbA1c \<8%, \> 8.3 mmol/L), or a random glucose level of \>180mg/dL (\> 10 mmol/L) is considered to have inadequately controlled diabetes and are not eligible for this study; however, such patients can become eligible in the future if their fasting glucose levels improve with medical treatment
* QTc prolongation (defined as a QTc interval \> 450 msec for males and \>470 msec for females) or other significant ECG abnormalities; NOTE: patients with clinically significant cardiac conduction abnormalities should be excluded, these include left bundle branch block (LBBB), 2nd or 3rd degree AV block, bifascicular block, sick sinus syndrome, Wolff-Parkinson-white syndrome, sinus bradycardia (\< 50bpm); however, patients with asymptomatic right bundle branch block (RBBB) or 1st degree AV block, in the absence of known cardiac disease (e.g. coronary, valvular) are not excluded
* Uncontrolled intercurrent illness including, but not limited to:
* Ongoing or active infection,
* Symptomatic congestive heart failure,
* Unstable angina pectoris,
* Uncontrolled symptomatic cardiac arrhythmia,
* Psychiatric illness/social situations that would limit compliance with study requirements
* Diagnosed to have any of the following condition(s), and/or have undergone any one of the following procedure(s) =\< 3 months prior to registration:
* Symptomatic thrombotic or hemorrhagic cerebral vascular accident
* Coronary bypass graft
* Angioplasty
* Myocardial infarction
* Patients having continuing \>= grade 2 adverse events (excluding alopecia) due to agents (chemotherapy or radiotherapy) administered \> 4 weeks prior to registration based on Common Terminology Criteria for Adverse Events (CTCAE version 4.0) =\< grade 1
* Any of the following:
* Pregnant women
* Nursing women
* Men or women of childbearing potential who are unwilling to employ adequate contraception
* NOTE: because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with MK-2206, breastfeeding should be discontinued if the mother is treated with MK-2206; 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
* HIV-positive patients on combination antiretroviral therapy; NOTE: HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with MK-2206; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy
* Recent major surgery =\< 4 weeks prior to registration (excluding the placement of vascular access), or minor surgery =\< 2 weeks prior to registration
* Any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption) that impairs patients ability to swallow MK-2206 tablets