The human lung airways are lined by the airway surface liquid (ASL). The ASL is either a layer of mucus or a two-layer liquid film consisting of the serous (outer) and the mucus (inner) layer. Owing to the Plateau-Rayleigh instability, the ASL can lead to airway closure, i.e. the occlusion of the airway due to the formation of a liquid plug. This is typical of distal airways, namely the bronchioles from the 7th generation onwards. In our simulations we focus on the fluid dynamics phenomena occurring during an airway closure, hence we assume the walls of the bronchioles as rigid. We isolate several elements of complexity to well comprehend their standalone effect on the airway closure. Indeed, we consider the airway closure with (i) a single-layer Newtonian clean film, (ii) a two-layer Newtonian clean film (iii) a single-layer surfactant-laden Newtonian film, (iv) a single-layer viscoelastic clean film, (v) a single-layer elastoviscoplastic clean film with and without kinematic hardening. Apart from the primary instability leading to airway closure, we focus on the post-coalescence wall stresses and secondary instabilities due to viscoelastic effects.