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 creatinine levels above institutional normal * Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of vorinostat will be determined following review of their case by the principal investigator * No other diagnosis of malignancy unless non-melanoma skin cancer, carcinoma in situ of the cervix, or a malignancy diagnosed \>= 5 years previously and currently with no evidence of disease; however - if the patient has had a previously diagnosed stage I/II malignancy of another type, consideration for recruitment may be made by the Cancer Therapy Evaluation Program (CTEP) senior investigator after discussion with local principal investigator (PI) and patient's physician * Confirmed availability of tumor tissue (either fresh or from paraffin block) from the primary tumor or metastatic site to be available to use on correlative studies * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * If the patient's tumor can be easily accessed, a pre-treatment biopsy will be mandatory Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier; more than 21 days from major surgery should have elapsed before the first dose of the study drug * Patients may not be receiving any other investigational agents or have received vorinostat in the past; patients should not have taken valproic acid for at least 4 weeks prior to enrollment * Inability to take oral medications on a continuous basis * Patients with active brain metastases should be excluded from this clinical trial; patients with previous brain metastases will be eligible if condition is treated and stable for \>= 1 month * History of allergic reactions attributed to compounds of similar chemical or biologic composition to SAHA * 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 * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with vorinostat * Patient is unable or unwilling to abide by the study protocol and to cooperate fully with the investigator or designee * Patient on current therapy with enzyme-inducing anticonvulsants