Romidepsin in Treating Patients With Locally Advanced or Metastatic Neuroendocrine Tumors

Inclusion Criteria:

* Histologically confirmed carcinoid tumor or islet cell neuroendocrine tumor

  * Well- or moderately-differentiated tumor
* Metastatic and/or locally advanced disease
* Measurable disease

  * Unidimensionally measurable lesion at least 20 mm by conventional techniques OR at least 10 mm by spiral CT scan
  * Lesions in a previously irradiated area are not considered measurable
  * No truly non-measurable lesions, including the following:

    * Bone lesions
    * Leptomeningeal disease
    * Ascites
    * Pleural or pericardial effusion
    * Lymphangitis cutis/pulmonis
    * Abdominal masses not confirmed and followed by imaging
    * Cystic lesions
* Ineligible for standard treatment
* Performance status - ECOG 0-1
* At least 6 months
* WBC \>= 3,000/mm\^3
* Absolute neutrophil count \>= 1,500/mm\^3
* Platelet count \>= 100,000/mm\^3
* Bilirubin =\< 1.5 mg/dL
* AST and ALT =\< 2.5 times upper limit of normal
* Creatinine =\< 1.5 mg/dL
* No New York Heart Association class III or IV congestive heart failure
* No myocardial infarction within the past year
* No uncontrolled dysrhythmias
* No poorly controlled angina
* No serious ventricular arrhythmia, defined as ventricular tachycardia or ventricular fibrillation \>= 3 beats in a row
* No left ventricular hypertrophy by EKG
* No other significant cardiac disease
* QTc \< 500 msec
* LVEF \> 40% by resting MUGA
* No prior allergic reaction attributed to compounds of similar chemical or biological composition to study drug
* No ongoing or active infection
* No psychiatric illness or social situation that would preclude study compliance
* No other concurrent uncontrolled illness
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* More than 4 weeks since prior immunotherapy (e.g., interferon alfa)
* More than 4 weeks since prior chemotherapy
* More than 12 weeks since prior hepatic artery chemoembolization unless liver lesions are not the only indicator lesions
* No prior FR901228 (depsipeptide)
* No more than 1 prior systemic chemotherapy regimen for carcinoid or islet cell tumor (other than hepatic artery chemoembolization)
* More than 4 weeks since prior oral or IV steroids (first 16 patients only)
* Concurrent long-acting octreotide allowed at standard doses if dose has been stable for the past 12 weeks

  * Concurrent subcutaneous octreotide for breakthrough use for symptomatic relief allowed
* No concurrent systemic steroids (first 16 patients only)
* More than 4 weeks since prior radiotherapy
* More than 4 weeks since prior investigational tumor-specific therapy
* No other prior histone deacetylase inhibitors (e.g., valproic acid)
* No concurrent hydrochlorothiazide
* No concurrent combination antiretroviral therapy for HIV-positive patients
* No other concurrent investigational or commercial agents or therapies for the malignancy