Vorinostat in Treating Patients With Locally Advanced, Recurrent, or Metastatic Adenoid Cystic Carcinoma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed locally advanced, recurrent or metastatic adenoid cystic carcinoma * 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 by chest x-ray, as \>= 10 mm with CT scan, or \>= 10 mm with calipers by clinical exam; all tumor measurements must be recorded in millimeters (or decimal fractions of centimeters) * Patients must have locally advanced and/or recurrent and/or metastatic disease not amenable to potentially curative surgery or radiotherapy; any prior number of chemotherapy regimens is allowed; a minimum of at least 4 weeks since prior chemotherapy or radiation therapy should have elapsed, 6 weeks if the last regimen included carmustine (BCNU) or mitomycin C * Life expectancy of greater than 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits (WNL) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal (ULN) * Creatinine within normal institutional limits or * Creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatin…