To start the discussion: I'd like to hear...your prediction.
If after a fight, the losing deadman has to give up a body part, what will Minatsuki-chan lose?
Yes, it's "random", but since the Crow already lost an eyeball, that can't be done twice. Taking something like a nose would ruin her pretty face, and a hand or some fingers might mess with her character design of being in manacles. So I say a foot, an ear, or nothing at all.
Likewise, how long do you think they'll keep up this rule? At first it's great for the dramatics and the grotesque element, but a little impractical to keep mutilating your characters (especially at the current rate of fights).
But we are ripe for something to happen to throw off the nice, insane little system that's set up.