Regorafenib in Treating Patients With Advanced or Metastatic Neuroendocrine Tumors

Inclusion Criteria: * Advanced metastatic, progressing carcinoid or pancreatic islet cell cancers * No prior targeted treatment (tx) or anti-angiogenic therapy; patients may have received one line of prior therapy with octreotide, locoregional therapy; continuation of concurrent octreotide is allowed; patients will be maintained on octreotide (sandostatin) for the duration of their treatment * Life expectancy of at least 12 weeks (3 months) * Subjects must be able to understand and be willing to sign the written informed consent form (ICF); a signed ICF must be appropriately obtained prior to the conduct of any trial-specific procedure * All acute toxic effects of any prior treatment have resolved to National Cancer Institute-Common Terminology Criteria for Adverse Events (NCI-CTCAE) version (v)4.0 grade 1 or less at the time of signing the informed consent form (ICF); exceptions to this include alopecia * Total bilirubin =\< 1.5 x the upper limits of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN (=\< 5 x ULN for subjects with liver involvement of their cancer) * Alkaline phosphastase limit =\< 2.5 x ULN (=\< 5 x ULN for subjects with liver involvement of their cancer) * Lipase =\< 1.5 x the ULN * Amylase =\< 1.5 x the ULN * Serum creatinine =\< 1.5 x the ULN * International normalized ratio (INR)/ partial thromboplastin time (PTT) \< 1.5 x ULN; (subjects who are treated with an agent such as warfarin or heparin will be allowed to participate provided that no prior evidence of underlying abnormality in coagulation parameters exists; close monitoring \[day 5 of cycle 1 and day 1 of each cycle\] is mandatory) will be performed until INR/PTT is stable based on a measurement that is pre-dose as defined by the local standard of care) * Platelet count \>= 100,000 /mm\^3 * Hemoglobin (Hb) \>= 9 g/dL * Absolute neutrophil count (ANC) \>= 1,500/mm\^3; blood transfusion to meet the inclusion criteria will not be allowed * Glomerular filtration rate (GFR) \>= 30 ml/min/1.73 m\^2 according to the Modified Diet in Renal Disease (MDRD) abbreviated formula * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of study drug; post-menopausal women (defined as no menses for at least 1 year) and surgically sterilized women are not required to undergo a pregnancy test; the definition of adequate contraception will be based on the judgement of the investigator * Subjects (men and women) of childbearing potential must agree to use adequate contraception beginning at the signing of the ICF until at least 3 months after the last dose of study drug; the definition of adequate contraception will be based on the judgment of the principal investigator or a designated associate * Subject must be able to swallow and retain oral medication * Southwest Oncology Group (SWOG) performance status 0-1 * Patients must have measurable disease Exclusion Criteria: * Previous assignment to treatment during this study; subjects permanently withdrawn from study participation will not be allowed to re-enter study * Uncontrolled hypertension (systolic pressure \> 140 mm Hg or diastolic pressure \> 90 mm Hg \[NCI-CTCAE v4.0\] on repeated measurement) despite optimal medical management * Active or clinically significant cardiac disease including: * Congestive heart failure - New York Heart Association (NYHA) \> class II * Active coronary artery disease * Cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin * Unstable angina (anginal symptoms at rest), new-onset angina within 3 months before randomization, or myocardial infarction within 6 months before randomization * Evidence or history of bleeding diathesis or coagulopathy * Any hemorrhage or bleeding event \>= NCI-CTCAE grade 3 within 4 weeks prior to start of study medication * Subjects with thrombotic, embolic, venous, or arterial events, such as cerebrovascular accident (including transient ischemic attacks) deep vein thrombosis or pulmonary embolism within 6 months of start of study treatment * Subjects with any previously untreated or concurrent cancer that is distinct in primary site or histology from carcinoid or pancreatic islet cancer except cervical cancer in-situ, treated basal cell carcinoma, or superficial bladder tumor; subjects surviving a cancer that was curatively treated and without evidence of disease for more than 3 years before randomization are allowed; all cancer treatments must be completed at least 3 years prior to study entry (i.e., signature date of the informed consent form) * Patients with pheochromocytoma * Known history of human immunodeficiency virus (HIV) infection or current chronic or active hepatitis B or C infection requiring treatment with antiviral therapy * Ongoing infection \> grade 2 NCI-CTCAE v4.0 * Presence of a non-healing wound, non-healing ulcer, or bone fracture * Renal failure requiring hemo-or peritoneal dialysis * Dehydration grade \>= 1 NCI-CTCAE v4.0 * Patients with seizure disorder requiring medication * Persistent proteinuria \>= grade 3 NCI-CTCAE v4.0 (\> 3.5 g/24 hrs, measured by urine protein:creatinine ratio on a random urine sample) * Interstitial lung disease with ongoing signs and symptoms at the time of informed consent * Pleural effusion or ascites that causes respiratory compromise (\>= NCI-CTCAE version 4.0 grade 2 dyspnea) * History of organ allograft (including corneal transplant) * Known or suspected allergy or hypersensitivity to any of the study drugs, study drug classes, or excipients of the formulations given during the course of this trial * Any malabsorption condition * Women who are pregnant or breast-feeding * Any condition which, in the investigator's opinion, makes the subject unsuitable for trial participation * Substance abuse, medical, psychological or social conditions that may interfere with the subject's participation in the study or evaluation of the study results * Patients with known brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to regorafenib or other agents used in study * 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 * Excluded therapies and medications, previous and concomitant * Concurrent anti-cancer therapy (chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, or tumor embolization) other than study treatment (regorafenib) * Prior use of regorafenib * Concurrent use of chemotherapy, radiotherapy or another investigational drug or device therapy (i.e., outside of study treatment) during, or within 4 weeks of trial entry (signing of the ICF) * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days before start of study medication * Use of any herbal remedy (e.g. St. John's wort \[Hypericum perforatum\])