Docetaxel With or Without Bintrafusp Alfa for the Treatment of Advanced Non-small Cell Lung Cancer

Inclusion Criteria: * Age \>= 18 years * Histological confirmation of non-small cell lung cancer (NSCLC) with advanced disease * Prior treatment required: * Anti-PD1/PD-L1 agent in combination with platinum-based chemotherapy * Measurable disease * NOTE: Tumor lesions in a previously irradiated area are not considered measurable disease; Disease that is measurable by physical examination only is not eligible * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Hemoglobin \>= 9.0 g/dL (obtained =\< 14 days prior to registration) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 14 days prior to registration) * Platelet count \>= 100,000/mm\^3 (obtained =\< 14 days prior to registration) * Total bilirubin =\< upper limit of normal (ULN) (obtained =\< 14 days prior to registration) * Alanine aminotransferase (ALT/serum glutamate pyruvate transaminase \[SGPT\]) and aspartate transaminase (AST/serum glutamic-oxaloacetic transaminase \[SGOT\]) =\< 1.5 x ULN (obtained =\< 14 days prior to registration) * Alkaline phosphatase \<= 2.5 x ULN (obtained =\< 14 days prior to registration) * Prothrombin time (PT)/international normalized ratio (INR)/activated partial thromboplastin time (aPTT) =\< 1.5 x ULN OR if patient is receiving anticoagulant therapy INR or aPTT is within target range of therapy (obtained =\< 14 days prior to registration) * Calculated creatinine clearance \>= 30 ml/min using the Cockcroft-Gault formula (obtained =\< 14 d…