Talactoferrin in Treating Patients With Relapsed or Refractory Non-Small Cell Lung Cancer or Squamous Cell Head and Neck Cancer

Inclusion Criteria: Histologically or cytologically confirmed, incurable metastatic relapsed/refractory NSCLC or relapsed/refractory, incurable, locally advanced or metastatic squamous head and neck cancer Head and neck squamous cell cancer patients must be able to be biopsied safely in clinic or by Stanford Interventional Radiology as determined by a Stanford Head and Neck Oncologist or Stanford Head and Neck Surgeon Hemoglobin (Hgb) \>= 9 gm/dl Platelets \>= 80,000/uL International normalized ratio (INR) =\< 1.5 Total bilirubin =\< 1.5 Creatinine =\< 1.5 Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2 times the upper limit of normal Failed therapy with at least one standard first line chemotherapy regimen, or intolerant of standard chemotherapy At least 4 weeks from the last chemotherapy, immunosuppressive/immunomodulatory therapy or investigational agent and 2 weeks from erlotinib or other non-immunogenic therapy Palliative radiotherapy to painful bony metastases must be completed at least 2 weeks prior to initiation of study treatment Brain metastases must be adequately treated (stable and asymptomatic) with surgery and/or radiation prior to enrollment and any steroids completed at least 3 weeks prior to study treatment initiation At least one un-irradiated target lesion measurable by Response Evaluation Criteria In Solid Tumors (RECIST) criteria At least one lesion amenable to repeat biopsy Life expectancy of at least 2 months Eastern Cooperative Oncology Group (ECOG) performance status 0-2 Absolute neutrophil count \>= 1,000/µl Absolute lymphocyte count \>= 800/µl Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: Concomitant chemotherapy, radiotherapy, immunosuppressive/immunomodulatory therapy or investigational agents Head and Neck Squamous Cell Carcinoma that can not be safely biopsied in Head and Neck Oncology Clinic or by Stanford Interventional Radiology as determined by a Stanford Head and Neck Oncologist or a Stanford Head and Neck Surgeon Co-morbid disease or incurrent illness that could affect patients' immune status or ability to comply with the study, but not limited to: * Renal failure requiring hemodialysis; * New York Heart Association (NYHA) Grade III or greater congestive heart failure; * Unstable angina; * Severe infectious or inflammatory illness; * Human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS); * Hepatitis (Hep) C positive (+) or Hep B surface antigen (+) Second malignancy with less than 5 years since documented clinical remission except for non-melanoma skin cancers or curatively treated cervical carcinoma in situ, superficial bladder cancer or early prostate cancer Prior history of allergic reaction to compounds of similar chemical or biologic composition to talactoferrin Inability to comply with study and/or follow-up procedures because of psychiatric or social situations Pregnant and nursing patients, sexually active patients (male and female) unwilling to practice contraception while on the study and at least 30 days after completion Oral corticosteroid therapy within 2 weeks prior to randomization or expected to be ongoing during the study Any gastrointestinal tract disease or other medical condition resulting in the inability to take oral medications