Considering more possessed like MC keep arriving, there's no point trying to hunt them all because there will always be another wave of possessed, so there will always be dungeon breaks. Some possessed probably went into hiding fearing for their life or something and will cause dungeon breaks until he dies of old age. The smarter thing to have done was to give them top tier treatment for revealing themselves on the requirement that they go into the maze. Then, instead of hiding because they fear for their lives and never having a hope of ending dungeon breaks, they would willingly go in themselves, but that's too late now that so many of them will probably never trust a sudden change in attitude.
