As far as mine go: Someone has a crucial piece, and basically if they die before a certain point it's game over. There are plenty of ways to avoid the death altogether, or at least reach the certain point before the character proceeds to drop dead. There are also ways to make it happen sooner, or interrupt the killing attempt.
If something were to happen that, uh, encouraged the culprit, a different character could well end up dead. An obvious example would be if Kit was correct in her yowling; as you say, she would be very much a target.
As far as other characters go: No, because (a) I would typically be against killing your character while you only had the one in play, and (b) due to all the arranging and shit that would have to make sense, I'd likely have to reveal the culprit to whoever's character I was killing, which would ruin the guessing fun while I proceeded to lock 'em out of the RP. Not cool!
If you managed to do something excessively stupid, like loudly discussing your suspicions in front of the one you thought to be suspicious, or that thing where the detective rounds up all the suspects and expects them to sit quietly while he reveals all, then I would likely arrange some form of game over. But... well, there'd hardly be any mystery to it, haha. And I'd probably try to warn you at least IC, if not OOC as well.
(Also, it would have to be really, really, reeeeeeally stupid.)