Capecitabine and Vorinostat in Treating Patients With Recurrent and/or Metastatic Head and Neck Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed SCCHN or NPC that is recurrent and/or metastatic and that is not amendable to curative therapy by surgery or radiation; SCCHN originating from the following sites are eligible: oral cavity, oropharynx, larynx, hypopharynx and paranasal sinus are eligible; for patients with a diagnosis of SCCHN of unknown origin, their eligibility must be reviewed and approved by the principal investigator * For patients with SCCHN, they may have received one prior targeted therapy for recurrent or metastatic disease (excluding histone deacetylase \[HDAC\] inhibitors) provided treatment is completed \> 4 weeks prior to enrollment; they may have received prior systemic chemotherapy (ie, induction, concurrent or adjuvant) for SCCHN as part of the initial multimodality treatment for locally advanced disease if the chemotherapy is completed \> 6 months prior to enrollment; patients are not eligible if they received fluorouracil (5-FU) or capecitabine previously as part of the initial multimodality treatment * Patients with NPC must have completed one prior chemotherapy regimen for recurrent or metastatic disease at least 4 weeks prior to enrollment; in addition, they may have received prior systemic chemotherapy (ie, induction, concurrent or adjuvant) for NPC as part of the initial multimodality treatment for locally advanced disease if the chemotherapy is completed \> 6 months prior to enrollment; patients are eligible if they received 5-FU as part of the initial multimodality treatment; patients are not eligible if they received capecitabine previously * 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 computed tomography (CT) scan; indicator lesions must not have been previously treated with surgery, radiation therapy or radiofrequency ablation unless there is documented progression after therapy * Patients must have completed any previous surgery or radiotherapy \>= 4 weeks prior to enrollment * Previously treated patients must have evidence of progressive disease, either clinically or radiographically, as assessed by the investigator * Eastern Cooperative Oncology Group (ECOG) performance status \< 2 (Karnofsky \> 60%) * Life expectancy of greater than 12 weeks * Absolute neutrophil count \>= 1.5 x 10\^9/L * Platelets \>= 100 x 10\^9/L * Total bilirubin =\< 1.25 times upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN or =\< 5 x ULN with documented liver metastases * Creatinine =\< 1.25 x ULN OR creatinine clearance \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels above 1.25 x ULN * 12-lead electrocardiogram (ECG) with normal tracing, or non-clinically significant changes that do not require medical intervention; corrected QT (QTc) interval \< 470 msec, and without history of Torsades de Pointes or other symptomatic QTc abnormality * Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity of vorinostat will be determined following review of their case by the principal investigator * Women of childbearing potential and men must be surgically sterilized, practicing abstinence, or agree to use 2 birth control methods prior to study entry and for the duration of study participation; the 2 birth control methods can be either be 2 barrier methods or a barrier method plus a hormonal method to prevent pregnancy; the following are considered adequate barrier methods of contraception: diaphragm or sponge, and condom; other methods of contraception such as copper intrauterine device or spermicide may be used; appropriate hormonal contraceptives will include any registered and marketed contraceptive agent that contains an estrogen and/or a progestational agent (including oral, subcutaneous, intrauterine, or intramuscular agents); 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 * Patients must be willing and able to comply with scheduled visits, treatment plan, laboratory tests and other study procedures * Willingness to discontinue taking any medications that are generally accepted to have a risk causing Torsades de Pointes during the study Exclusion Criteria: * Past or current malignancy other than SCCHN or NPC, except for: * Cervical carcinoma Stage 1B or less * Non-invasive basal cell and squamous cell skin carcinoma * Malignant melanoma with a complete response of a duration of \> 10 years * Radically treated prostate cancer (prostatectomy or radiotherapy) with normal prostate specific antigen (PSA), and not requiring ongoing anti-androgen hormonal therapy * Other cancer diagnosis with a complete response of duration of \> 5 years * Patients may not be receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial * Prior use of capecitabine is not allowed * Prior and concomitant treatment with HDAC inhibitors (such as valproic acid) are not allowed * History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat or other agents used in study * Patients who are unable to take oral medications and / or who have a clinical or radiological diagnosis of bowel obstruction are ineligible * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, active peptic ulcer disease, myocardial infarction within 6 months prior to entry, congestive heart failure, symptomatic congestive heart failure, active cardiomyopathy, unstable angina pectoris, cardiac arrhythmia, uncontrolled hypertension 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 * Human immunodeficiency virus (HIV)-positive patients are ineligible * Patients with known dihydropyrimidine dehydrogenase (DPD) deficiency are excluded