Dasatinib in Treating Patients With Recurrent or Metastatic Head and Neck Cancer

Inclusion Criteria: * Patient has histologically proven squamous cell carcinoma of the head and neck that is recurrent after surgery and/or radiation therapy or chemoradiation therapy or is metastatic and disease must be measurable by RECIST criteria * Patients must have measurable disease as defined by RECIST criteria * Patients have received =\< 1 prior chemotherapeutic regimen for recurrent or metastatic disease * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin (Hgb) \>= 9.0 g/dL * Total bilirubin =\< 1.5 X upper limit of normal * Albumin \>= 2.5 g/dL * Aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) =\< 1.5 X upper limit of normal * Creatinine =\< 3 mg/dl * Paraffin embedded tumor tissue that is appropriate for immunohistochemistry (IHC) and fluorescent in situ hybridization (FISH) analysis must be available or patient must be amenable to biopsy to obtain tissue for the study * Ability to understand and the willingness to sign a written informed consent document * Patient must not be pregnant or breastfeeding; all sexually active females of child-bearing potential and all sexually active males with sexual partners of child-bearing potential should practice contraception (e.g. barrier, hormonal, intrauterine device \[IUD\]) or sexual abstinence while in the study and for two months following completion of therapy * Brain metastases permitted provided the patient does not require anticonvulsants or corticosteroids, or has been off them at least 7 days; patients with brain metastases must be either \> 4 weeks beyond cranial irradiation or must be felt not to require it at that time * The patient's O2 saturation must be \>= 92% on room air Exclusion Criteria: * Chemotherapy or palliative radiotherapy for recurrent and/or metastatic disease within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or failure to recover to at least grade 1 from adverse events due to agents administered more than 4 weeks earlier; concomitant chemoradiation therapy within 6 weeks prior to entering the study or failure to recover to at least grade 1 from adverse events due to agents administered more than 4 weeks earlier * Other anti-neoplastic agents, i.e., cytotoxic chemotherapy, immunotherapy, radiotherapy or investigational therapy, used to treat the primary disease will not be allowed during the study; local radiation (excluding radiotherapy to the target lesion) for supportive reasons involving a small radiation field may be allowed * Patient has a history of uncontrolled or severe medical disease which could compromise participation in the study such as uncontrolled diabetes (fasting blood glucose \> 200 mg/dl), uncontrolled hypertension (systolic blood pressure \[BP\] \> 160 or diastolic BP \> 100 mmHg), severe infection (bacterial infection requiring intravenous \[IV\] antibiotics or human immunodeficiency virus \[HIV\]), angina at rest, congestive heart failure New York Heart Association (NYHA) class III or IV, ventricular arrhythmias requiring therapy, myocardial infarction within 6 months, \> grade 2 neuropathy * Patients may not be receiving any other investigational agents * Patients who require concurrent treatment with any medications or substances that are potent inhibitors or inducers of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) are ineligible; efforts should be made to switch patients with gliomas or brain metastases who are taking enzyme-inducing anticonvulsant agents to other medications * Echocardiogram less than institutional normal measured by echocardiogram for subjects with history of congestive heart failure, symptoms of congestive heart failure, clinical evidence suggesting impaired cardiac function * Patients may not have any clinically significant cardiovascular disease including the following: * Myocardial infarction or ventricular tachyarrhythmia within 6 months * Prolonged correct QT interval (QTc) \> 480 msec (Fridericia correction) * Major conduction abnormality (unless a cardiac pacemaker is present) * Pregnant women and women who are currently breast-feeding may not participate in this study; all women of childbearing potential must have a negative pregnancy test within 72 hours prior to enrolling in the study; postmenopausal women must be amenorrheic for at least 12 months to be considered of non-childbearing potential * Patients having pleural effusion