Ziv-Aflibercept in Treating and Computed Tomography Perfusion Imaging in Predicting Response in Patients With Pancreatic Neuroendocrine Tumors That Are Metastatic or Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have histologically or cytologically confirmed low or intermediate grade pancreatic NET; patients with neuroendocrine tumors associated with multiple endocrine neoplasia type 1 (MEN1) syndrome will be eligible * Patients must have unresectable or metastatic disease * Patients must have at least one measurable site of disease according to RECIST 1.1 that has not been previously irradiated * Patients must have at least one lesion suitable for perfusion CT; the lesion should be greater than or equal to 3 cm in size in the cranial caudal direction * Patient must have no contraindication for CT with iodinated contrast * Patients who are on a somatostatin analogue for control of hormonal syndromes must be on a stable dose (no change in mg dose of long acting octreotide or lanreotide, changes in dosing interval of +/- 1 week is allowed) for 2 months prior to date of study entry * Women of child-bearing potential must have a negative serum pregnancy test within 7 days prior to date of study entry; women who have had menses within the past 2 years, who have not had a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy are considered to be of child-bearing potential; patients with elevated human chorionic gonadotropin (hCG) at baseline that is judged to be related to the tumor are eligible if hCG levels do not show the expected doubling when repeated 5-7 days later, or pregnancy has been ruled out by vaginal ultrasound * Any number of prior lines of systemic anti-neoplastic therapy are allowed; treatment with =\< 1 prior VEGF inhibitor will be allowed * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Urine protein:creatinine ratio =\< 1.0 OR 24-hour urine protein =\< 500 mg (24-hour total urine protein only need be obtained if urine protein:creatinine ratio \< 1.0) * Patients must have prothrombin time (PT)/international normalized ratio (INR)/partial thromboplastin time (PTT) within 1.2 x the upper limit of normal * Patients must have resting blood pressure (BP) no greater than 140 mmHg (systolic) or 90 mmHg (diastolic) for eligibility; initiation or adjustment of BP medication is permitted prior to study entry * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Less than 28 days elapsed from prior radiotherapy, from prior surgery and prior chemotherapy to the time of randomization; less than 42 days elapsed from prior major surgery to the time of randomization * Adverse events (with exception of alopecia, peripheral sensory neuropathy and those listed in specific exclusion criteria) from any prior anti cancer therapy of grade \> 1 (National Cancer Institute Common Terminology Criteria \[NCI CTCAE\] version \[v.\]4.0) * Eastern Cooperative Oncology Group (ECOG) performance status (PS) \> 2 * History of brain metastases, uncontrolled spinal cord compression, or carcinomatous meningitis or new evidence of brain or leptomeningeal disease * Other prior malignancy; adequately treated basal cell or squamous cell skin cancer, carcinoma in situ of the cervix or any other cancer from which the patient has been disease free for \> 5 years are allowed * Participation in another clinical trial and any concurrent treatment with any investigational drug within 30 days prior to study entry * Any of the following within 6 months prior to study entry: myocardial infarction, severe/unstable angina pectoris, coronary/peripheral artery bypass graft, New York Heart Association (NYHA) class III or IV congestive heart failure, stroke or transient ischemic attack * Any of the following within 3 months prior to study entry: grade 3-4 gastrointestinal bleeding/hemorrhage, treatment resistant peptic ulcer disease, erosive esophagitis or gastritis, infectious or inflammatory bowel disease, diverticulitis, pulmonary embolism or other uncontrolled thromboembolic event * Occurrence of deep vein thrombosis within 4 weeks, prior to study entry * Acquired immuno deficiency syndrome (AIDS-related illnesses) or known human immunodeficiency virus (HIV) disease requiring antiretroviral treatment * Any severe acute or chronic medical condition, which could impair the ability of the patient to participate to the study or to interfere with interpretation of study results * Pregnant or breast feeding women; positive pregnancy test (serum or urine beta-human chorionic gonadotropin \[HCG\]) for women of reproductive potential * Patient with reproductive potential (female and male) who do not agree to use an accepted effective method of contraception (hormonal or barrier methods, abstinence) during the study treatment period and for at least 3 months following completion of study treatment; for female patient enrolled, the following methods of contraception are acceptable: oral contraceptives accompanied by the use of a second method of contraception, or intra uterine device (IUD) or women who are surgically sterile, or women who are post -menopausal or other reasons have no chance of becoming pregnant * Absence of signed and dated Institutional Review Board-approved patient informed consent from prior to enrollment in the study * EXCLUSION CRITERIA RELATED TO ZIV-AFLIBERCEPT * Urine protein-creatinine ratio (UPCR) \> 1 urinalysis or total urine protein \> 500 mg/24 hours (h) * Serum creatinine \> 1.5 x upper limit of normal (ULN); if creatinine 1.0-1.5 x ULN, creatinine clearance, calculated according to Cockcroft-Gault formula, \< 60 ml/min will exclude the patient * History of uncontrolled hypertension, defined as systolic blood pressure \> 150 mmHg while simultaneous diastolic blood pressure \> 100 mmHg, or systolic blood pressure \> 180 mmHg when diastolic blood pressure \< 90 mmHg, on at least 2 repeated determinations on separate days within 3 months prior to study enrollment * Patients on anticoagulant therapy with unstable dose of warfarin and/or having an out-of- therapeutic range INR (\> 3) within the 4 weeks prior to study entry * Evidence of clinically significant bleeding diathesis or underlying coagulopathy (e.g. INR \> 1.5 without vitamin K antagonist therapy), non-healing wound