Elisabeth, while you could technically could stumble into someone while Drained and break off a Killing Blow, this goes against the Spirit of the Rules. The reason you can only break a Killing Blow with a weapon is that everything we do in the game is a representation of what you might be able to do if our real world had magic. Being Drained represents being so injured/weakened that you can barely walk, but it lets you get off the battlefield. Slowly.

Think of it this way: if you've ever been about to pass out, you know what a struggle it is to remain upright and keep moving forward towards a place you can collapse without hurting yourself. In such a state, you would be in no condition to stop some scoundrel from stealing a lady's purse, despite the fact that you could kick his butt if you were feeling better.

Even though Elizabeth is perfectly fine, when Kitten gets Drained, you should act like you're about to fall over. That's this is a role-playing game rather than a mosh pit. :)