Pazopanib Hydrochloride in Treating Patients With Advanced Neuroendocrine Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed low or intermediate grade carcinoid or islet cell carcinoma; patients with carcinoid or islet cell carcinoma associated with multiple endocrine neoplasia (MEN)1 syndrome will be eligible and entered in the islet cell cohort * 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 \>= 20 mm with conventional techniques or as \>= 10 mm with spiral CT scan * Patients may have received 0 or 1 prior cytotoxic therapy; chemotherapy used as a radiosensitizer will be considered one prior chemotherapy regimen; patient must not have received prior bevacizumab or any other therapy targeting vascular endothelial growth factor (VEGF) or VEGF receptors (i.e., SU11248, PTK787/ZK222584, Sorafenib, GW786034) * Patients must be on a stable dose of somatostatin analogue for 2 months prior to start of protocol; octreotide dose not count toward prior therapy * Prior radiation therapy is permitted; a recovery period of at least 4 weeks after completion of radiotherapy is required prior to enrollment * Patients may have received prior interferon (not counted toward prior cytotoxic chemotherapy) * Patients may have received prior therapy targeting v-kit Hardy-Zuckerman 4 feline sarcoma viral oncogene homolog (c-kit), c-abl oncogene 1, non-receptor tyrosine kinase (abl), platelet-derived growth factor receptor (PDGFR), or epidermal growth factor receptor (EGFR) (imatinib, gefitinib, erlotinib, cetuximab; not counted toward prior cytotoxic chemotherapy) * Patients must have unresectable or metastatic disease * Eastern Cooperative Oncology Group (ECOG) performance status of 0, or 1 (Karnofsky \>= 70%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 120,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 X institutional upper limit of normal * Creatinine =\< 2.0 OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal (calculated by Cockcroft Gault formula) * 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 * Women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation; women of child-bearing potential must have a negative blood pregnancy test prior to study entry; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately; acceptable contraceptive methods, when used consistently and in accordance with both the product label and the instructions of the physician, are as follows: * An intrauterine device with a documented failure rate of less than 1% per year * Vasectomized partner who is sterile prior to the female patient's entry and is the sole sexual partner for that female * Complete abstinence from sexual intercourse for 14 days before exposure to investigation product, through the clinical trial, and for at least 21 days after the last dose of investigational product * Double-barrier contraception (condom with spermicidal jelly, foam suppository, or film; diaphragm with spermicide; or male condom and diaphragm with spermicide) * Note: Oral contraceptives are not reliable due to potential drug-drug interaction * Ability to understand and the willingness to sign a written informed consent document * Ability to swallow and retain oral medication Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks prior to study enrollment; at least 4 weeks must have elapsed since any major surgery prior to study enrollment * Patients may not be receiving any other investigational agents * Patients with corrected QT (QTc) \> 480 msecs * Patients with greater than 1+ (\>= 100 mg/dl) proteinuria on two consecutive routine urinalysis taken at least 1 week apart are ineligible * Certain medications that act through the cytochrome P450 (CYP450) system are specifically prohibited in patients receiving GW786034 (pazopanib) because in vitro data indicate that the agent has the potential to interact with the cytochrome P450 isoenzymes; certain other agents should be used with caution * Patients with any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for intravenous \[IV\] alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease) that impairs their ability to swallow and retain GW786034 (pazopanib) tablets are excluded * Patients with any of the following conditions are excluded: * Serious or non-healing wound, ulcer, or bone fracture * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days of treatment * History of known active diverticulitis within the past 3 months * Any history of cerebrovascular accident (CVA) within the last 6 months * Current use of therapeutic warfarin; Note: Low molecular weight heparin and prophylactic low-dose warfarin are permitted; PT/PTT must meet the inclusion criteria * History of myocardial infarction, cardiac arrhythmia, admission for unstable angina, cardiac angioplasty or stenting within the last 12 weeks * History of venous thrombosis in last 12 weeks * Class III or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system; a patient who has a history of class II heart failure and is asymptomatic on treatment may be considered eligible * Patients with known brain metastases should be excluded from this clinical trial * No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, or other adequately treated in situ cancer, or any other cancer from which the patient has been disease free for five years * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with GW786034 (pazopanib); these potential risks may also apply to other agents used in this study * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Uncontrolled diarrhea (8 or more bowel movements per day)