Depsipeptide in Unresectable Recurrent or Metastatic Squamous Cell Carcinoma of the Head and Neck

Inclusion Criteria: * histologically or cytologically confirmed squamous cell cancer of the head and neck (MedDRA code 90002024), excluding nasopharyngeal primaries, which is unresectable or metastatic; the disease must be incurable with surgery or radiation therapy; the tumor should preferably be present at the primary site, and it must be accessible to planned biopsy methods * Measurable disease by RECIST, * May have received any number of prior systemic chemotherapy regimen for unresectable, recurrent or metastatic disease; if the only site of measurable disease is a previously irradiated area, the patient must have documented progressive disease or biopsy-proven residual carcinoma; persistent disease after radiotherapy must be biopsy-proven at least 8 weeks after the completion of radiotherapy * Life expectancy of greater than 3 months * Normal organ and marrow function as defined by the following labs performed =\< 2 weeks of study entry: * Leukocytes ≥ 3,000/uL * Absolute Neutrophil Count ≥ 1,500/uL * Hemoglobin ≥ 10 gm% * Platelets ≥ 100,000/uL * Total Bilirubin =\< 1.5 X upper normal institutional limit * AST(SGOT)/ALT(SGPT) =\< 2.5 X upper normal institutional limits * Creatinine within normal institutional limits OR creatinine clearance ≥ 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * PT/PTT =\< 1.1X upper normal institutional limits * Calcium within normal institutional limits * CPK, Troponin within normal institutional limits * Uric Acid within normal institutional limits * Ability to understand and the willingness to sign a written informed consent document; in addition to consent for the therapy, patients must give consent to required pre- and post-therapy blood and tissue samples; Exclusion Criteria: * Patients should not have had prior therapy with depsipeptide and may not be receiving any other investigational agents or drugs known to have histone deacetylase inhibitor activity such as sodium valproate * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * Significant cardiac disease including congestive heart failure that meets New York Heart Association (NYHA) class III and IV definitions (see Appendix II), history of myocardial infarction within one year of study entry, uncontrolled dysrhythmias, or poorly controlled angina * History of serious ventricular arrhythmia (VT or VF, \> 3 beats in a row), QTc \> 500 msec, or LVEF \< 40% * Patients may not be co-medicated with an agent that causes QTc prolongation; - Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, or psychiatric illness/social situations that would limit compliance with study requirements * Not pregnant or lactating * History of HIV infection