It is well-understood that the usage of facemasks provides protection from transmission of viral loads through exhalation and inhalation of respiratory droplets. Although three-layer masks are advised for usage, many commonly available or homemade masks contain only single and double layers. In this study, we show through detailed physics-based analyses and high-speed imaging that high momentum cough droplets on impingement on single- and double-layer masks can lead to significant partial penetration and more importantly atomization into numerous much smaller daughter droplets, thereby increasing the total population of the aerosol, which can remain suspended for a longer time. The possibility of secondary atomization of high momentum cough droplets due to impingement, hydrodynamic focusing and extrusion through the microscale pores in the fibrous network of the mask has not been explored before. Interestingly, this unique mode of aerosol generation poses the risk of infection, as demonstrated in this work.