If you balefire your companion in a circle then they would die. The link being broken before you started to weave, but the weave still having existed, I'd say that if you were drawing as much of the power as possible that you'd then end up having drawn that power yourself, and burning yourself out.

But it is very possible I am talking complete nonsense and I hope someone comes along with some properly thought-through theories. It's an interesting question.

I don't think you could be burned out because the person would no longer be part of the link. This sparked another thought, what would a battle be like between two circles of channelers fighting with balefire at varying strenghts. Would be very complex.

But I maybe over thinking this