Hee!  What a dastardly idea!  You could have all hostile
creatures encountered *always* shift level with the character,
until the character kills them or they find some reason to be
more interested in something else than the character.

So, you meet BigNasti out of depth on level 9, run upstairs,
and he chases you back to level 8, and 7, and 6 ...

This could make an interesting subgame where the successful player
goes "what have I met that wasn't hostile, but which will fight
BigNasti?" or "what have I met that BigNasti would rather eat
than me?"  And leads the chasing creature back to it.

It could also make for interesting variations where the player
(advertently or otherwise) leads something back to town and leaves -
and when he comes back it's eaten all the people.  Bonus points
if it was a vampire and now all the townspeople are too, or
something like that!

                                Bear