This question https://physics.stackexchange.com/a/193472/93888 explains what would happen after a cartridge is ignited: the bullet gets propelled by the gases in one direction and the cartridge (with the person, in the case of the question) in the opposite direction.
But would a cartridge explode/ignite if hit from the side (the rear part where the gunpowder is, not the side of the bullet) or the front by a bullet? Or is the rear the only side able to start the reaction?