Sapanisertib in Treating Patients With Metastatic or Refractory Pancreatic Neuroendocrine Tumor That Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have unresectable or metastatic, histologically confirmed low or intermediate grade (Klimstra Criteria) pancreatic neuroendocrine tumor (PNET) with radiological evidence of disease progression since last treatment * Refractory disease to treatment with an mTOR inhibitor * Patients with 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, are ineligible * Disease that is currently not amenable to surgery, radiation, or combined modality therapy with curative intent * Patients must not have poorly differentiated neuroendocrine carcinoma, high-grade neuroendocrine carcinoma, adenocarcinoid, goblet cell carcinoid and small cell carcinoma * Patients must have measurable disease * Documented radiological evidence for disease progression (measurable or nonmeasurable) =\< 12 months prior to enrollment * NOTE: If patient has had previous radiation to the marker lesion(s), there must be evidence of progression since the radiation; at least one measurable lesion as per Response Evaluation Criteria in Solid Tumors (RECIST) * Prior or concurrent therapy with somatostatin analogue (SSA) is permitted; a stable dose at least 2 months prior to study start and must continue on the stable dose while receiving study treatment; SSA is not considered as systemic treatment * Recovered from adverse events to grade 1 or less toxicity according to Common Terminology Criteria for Adverse Events version 4.0 (CTCAE 4.0) due to agents administered previously * NOTE: Chemotherapy-induced alopecia and grade 2 neuropathy are acceptable * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Patients must be able to swallow intact capsules * Leukocytes \>= 3,000/mm\^3 (within less than or equal to 14 days prior to registration) * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (within less than or equal to 14 days prior to registration) * Hemoglobin \>= 10 g/dL (within less than or equal to 14 days prior to registration) * Platelets \>= 100 x 10\^9/L (within less than or equal to 14 days prior to registration) * Total serum bilirubin =\< institutional upper limit of normal (ULN) (within less than or equal to 14 days prior to registration) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN (within less than or equal to 14 days prior to registration) * Serum creatinine =\< 1.5 X institutional ULN and creatinine clearance \>= 60 ml/min (within less than or equal to 14 days prior to registration) * NOTE: Creatinine clearance must be calculated using the Cockcroft-Gault equation * Glycosylated hemoglobin (HbA1c) \< 7.0% (within less than or equal to 14 days prior to registration) * Fasting serum glucose =\< 130 mg/dL (within less than or equal to 14 days prior to registration) * Fasting triglycerides =\< 300 mg/dL (within less than or equal to 14 days prior to registration) * Diabetics are allowed if: * Fasting blood glucose (FBG) =\< 130 mg/dL (mmol/L), OR * HbA1c =\< 7% * Women must not be pregnant or breast-feeding due to potential harm to the fetus from MLN0128 (TAK-228); all females of childbearing potential must have a blood test or urine study within 7 days of registration to rule out pregnancy; a female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Women of child-bearing potential and men must agree to practice 1 highly effective method of contraception and 1 additional effective (barrier) method of contraception, at the same time, from the time of signing the informed consent through 90 days (for female patients) and 120 day (for male patients) after the last dose of study drug, or agree to completely abstain from heterosexual intercourse; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men must agree not to donate sperm during the course of this study or within 120 days after receiving their last dose of study drug * Patients who have a history of brain metastasis are eligible for the study provided that all the following criteria are met: * Brain metastases which have been treated * No evidence of disease progression for \>= 3 months before the first dose of study drug * No hemorrhage after treatment * Off-treatment with dexamethasone for 4 weeks before administration of the first dose of TAK-228 * No ongoing requirement for dexamethasone or anti-epileptic drugs * Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care Exclusion Criteria: * Patient is INELIGIBLE if patient discontinued prior mTOR inhibitor due to toxicity * Patients must NOT have radiotherapy, or major surgery or active drug therapy for pNET (SSA permitted) within 4 weeks prior to study treatment start * Patient must NOT have had previous treatment with any PI3K or AKT inhibitor * NO hepatic artery embolization or cryoablation/radiofrequency ablation of hepatic metastasis within 2 months of study treatment start * Patients must NOT have previous or concurrent malignancy within 2 years; exceptions are made for patients who meet any of the following conditions: * Adequately treated basal cell or squamous cell skin cancer, superficial bladder cancer OR * Adequately treated stage I or II cancer currently in complete remission, or any other cancer that has been in complete remission for at least 2 years * No more than 3 prior systemic treatment regimens for advanced PNET * Patients with a history of the following within =\< 6 months of study entry are NOT eligible: * Ischemic myocardial event, including angina requiring therapy and artery revascularization procedures * Ischemic cerebrovascular event, including transient ischemic attack (TIA) and artery revascularization procedures * Requirement for inotropic support (excluding digoxin) or serious (uncontrolled) cardiac arrhythmia (including atrial flutter/fibrillation, ventricular fibrillation or ventricular tachycardia) * New York Heart Association (NYHA) class III or IV heart failure * Pulmonary embolism * Patients with known significant active cardiovascular or pulmonary disease at the time of study entry are INELIGIBLE including: * Uncontrolled hypertension (i.e., systolic blood pressure \>180 mm Hg, diastolic blood pressure \> 95 mm Hg); use of anti-hypertensive agents to control hypertension before cycle1 day 1 is allowed * Pulmonary hypertension * Uncontrolled asthma or oxygen (O2) saturation \< 90% by arterial blood gas analysis or pulse oximetry on room air * QT syndrome, or torsades de pointes * Significant valvular disease; severe regurgitation or stenosis by imaging independent of symptom control with medical intervention, or history of valve replacement * Medically significant (symptomatic) bradycardia * History of arrhythmia requiring an implantable cardiac defibrillator * Baseline prolongation of the rate-corrected QT interval (QTc) (e.g., repeated demonstration of QTc interval \> 480 milliseconds, or history of congenital long * Patients with known manifestations of malabsorption due to prior gastrointestinal (GI) surgery, GI disease, or for an unknown reason that may alter the absorption of MLN0128 (TAK-228) are INELIGIBLE * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are INELGIBLE because of the potential for pharmacokinetic interactions with MLN0128 (TAK-228) * NO treatment with strong inhibitors and/or inducers of cytochrome P450 (CYP) 3A4, or CYP2C19 within 1 week preceding the first dose of study drug * NO patients receiving systemic corticosteroids (either intravenous \[IV\] or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug * Patients CANNOT have daily or chronic use of a proton pump inhibitor (PPI) and/or having taken a PPI within 7 days before receiving the first dose of study drug