Vorinostat in Treating Patients With Locally Recurrent or Metastatic Cancer of the Urothelium

Inclusion Criteria: * Patients must have a pathological diagnosis of transitional cell carcinoma of the bladder or urothelium with less than 25% component of other cell types such as small cell, neuroendocrine or squamous cell carcinoma; archival tumor tissue must be available for classification and correlates as described in this protocol or otherwise the patient must be willing to undergo biopsy prior to trial entry * 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 with boney metastases are allowed to participate in the study provided they also have non-osseous disease that is measurable * Patients must have recurred or progressed on or subsequent to platinum-based chemotherapy in the adjuvant or advanced setting; patients treated with a second line of chemotherapy may be included provided more than six months elapsed from the completion of the first line of chemotherapy to the start of the second; patients may have had any number of prior intravesical therapies for superficial bladder cancer; patients may also have had one experimental biologic therapy for their metastatic urothelial cancer provided this was not an agent known to act through histone deacetylation or demethylation; these compounds include sodium butyrate, trichostatin A (TSA), trapoxin (TPX), MS-27-275 and depsipeptide * Life expectancy of greater than 3 months * ECOG performance status =\< 2 (Karnofsky \>= 60%) * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * AST (SGOT)/ALT (SGPT) =\< 2.5 x institutional upper limit of normal unless there are liver metastases in which case AST/ALT must be =\< 5 x the upper limits of institutional normal * Creatinine =\< 1.5 times normal institutional limits OR creatinine clearance \>= 40 mL/min/1.73 m\^2 for patients with creatinine levels above 1.5 times institutional normal * Eligibility of patients receiving any medications or substances known to effect or with the potential to effect the activity or pharmacokinetics of SAHA will be determined following review by the principal investigator * 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 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 * Patients may not be receiving any other investigational agents * 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 * History of allergic reactions attributed to compounds of similar chemical or biologic composition to SAHA; these compounds include sodium butyrate, trichostatin A (TSA), trapoxin (TPX), MS-27-275 and depsipeptide * Prior treatment with more than 2 cytotoxic chemotherapy regimens for urothelial transitional cell cancer * 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 stud; breastfeeding should be discontinued if the mother is treated with SAHA * HIV-positive patients receiving combination antiretroviral therapy are ineligible * Patients should not have taken valproic acid for at least two weeks prior to study entry