Im guessing the goal is to get the axe as deep into the abyss or whatever, as they possibly can. The deeper it is, the less likely the demon inside can get back to the material plane when it escapes. Im pretty sure they all know, even if they havent said it, that its a suicide mission. Its not like there really is an end point where they can dust off their hands, say, good enough, and try walking back out of hell. So keep going till they get dragged down and hope its enough. Eternal torment sure, but at least they saved the world.