Bortezomib With or Without Irinotecan in Treating Patients With Locally Recurrent or Metastatic Squamous Cell Carcinoma of the Head and Neck

Inclusion Criteria: * Patients may have had one (0-1) prior chemotherapy regimen for recurrent or metastatic SCCHN; chemotherapy for recurrent or metastatic disease must have been completed at least 4 weeks prior to study entry * Patients must not have been previously treated with irinotecan or bortezomib * Patients must not be receiving radiation treatment * Patients must have histologically confirmed squamous cell carcinoma of the head and neck * Patients must have biopsy for histological confirmation of recurrent or metastatic disease if disease is now recurrent or metastatic after prior disease free-interval * NOTE: If patient has had a complete response (of any duration) but now has suspected recurrent disease (regardless of the time interval), the patient will need a biopsy for confirmation of SCCHN * Disease must not be amenable to potentially curative local therapies or patient must have refused such options * Patients must not have nasopharyngeal subtypes WHO II or III. Patients may have nasopharyngeal WHO I; salivary gland primaries are excluded from study SUBTYPES OF NASOPHARYNGEAL CARCINOMA (NPC) WHO type 1 - keratinizing SCC WHO type 2 - nonkeratinizing epidermoid carcinoma WHO type 3 - undifferentiated carcinoma * Patients must have measurable disease * Baseline measurements and evaluations must be obtained within 4 weeks of registration to the study * Measurable disease limited to a pre-irradiated location must be biopsy proven to be squamous cell carcinoma * Must have at least one objective measurable disease parameter; baseline measurements and evaluations must be obtained within 4 weeks of registration to the study; all areas of disease should be recorded and mapped out in order to assess response and uniformity of response to therapy * Radiographic findings are acceptable providing that clear-cut measurement can be made * Measurable disease limited to a pre-irradiated location must be biopsy-proven to be squamous cell carcinoma * Patients must have ECOG performance status 0 or 1 * Patients must not have grade 2 or higher peripheral neuropathy within 2 weeks of study entry * Leukocytes \>= 3,000/uL * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin within normal institutional limits * AST(SGOT) and ALT(SGPT) =\< 2.5 x institutional upper limit of normal * Creatinine within normal institutional limits OR * Creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Patients must have had no prior invasive malignancy unless the disease-free interval is 5 years or more * Women must not be pregnant or breast-feeding due to the fact that the teratogenic or abortifacient effects of PS-341are unknown; the effect of PS-341 on the nursing infant are also unknown; all females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy * Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception 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 * Patients with known brain metastases will 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 * Patients must not have history of allergic reactions to PS-341 or allergic reaction attributed to compounds of similar chemical or biologic composition to PS-341 including boron or mannitol * Patients must not have uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, unstable angina pectoris, or psychiatric illness/social situations that would limit compliance with study requirements * ELIGIBILITY FOR RE-REGISTRATION TO ARM A (FOR ARM B PATIENTS AT THE TIME OF PROGRESSION * Patients must have ECOG performance status 0 or 1 * Leukocytes \>= 3,000/uL * Absolute neutrophil count \>- 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin within normal institutional limits * AST(SGOT) and ALT(SGPT) =\< 2.5 x institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Patients with known brain metastases will 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