Erlotinib Hydrochloride and Cabozantinib-s-Malate Alone or in Combination as Second or Third Line Therapy in Treating Patients With Stage IV Non-small Cell Lung Cancer

PRIMARY OBJECTIVES: I. To compare the progression-free survival (PFS) associated with patients treated with erlotinib (erlotinib hydrochloride) versus (vs) erlotinib plus cabozantinib (cabozantinib-s-malate). II. To compare the PFS associated with patients treated with erlotinib vs cabozantinib. SECONDARY OBJECTIVES: I. To evaluate overall survival in the three treatment arms. II. To evaluate best objective response rate in the three treatment arms. III. To define the toxicity associated with each regimen. IV. To conduct correlative science studies that will help to select predictive biomarkers of response to therapy, including mesenchymal-epidermal transition (MET) expression and potentially other tissue biomarkers, plasma biomarkers, and bone scans. OUTLINE: Patients are randomized to 1 of 3 treatment arms. ARM A (erlotinib): Patients receive erlotinib orally (PO) daily on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. ARM B (cabozantinib): Patients receive cabozantinib PO daily on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. ARM C (erlotinib+cabozantinib): Patients receive erlotinib as patients in Arm A and cabozantinib as patients in Arm B. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. ARM Z: Patients achieving disease progression in Arm A or Arm B may receive erlotinib and cabozantinib as patients in Arm C. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months for 2 years and then every 6 months for 3 years.