how would you do a camcorder style FPS where you never see the monster?

Unless you're thinking of a game based around escaping from a monster... Nothing creates tension like carrying an AK through a dark building knowing there's a huge monster outside that could smash through from the outside and block off an exit/try to kill you at any moment... and I can see some EPIC level plans for that sort of thing... sort of a really long, and slightly bigger version of blast pit.