Poor kid.
I think that the mother had some crazy idea that she could scare her daughter into behaving better, since a similar ruse worked for a friend's child. However, I think letting a young child believe you will abandon them is a terrible idea that's bound to backfire in all sorts of ways.
I have to say I have done something sort of similar before when my daughter was running away from me and I couldn't catch her. I called out after her, "Have a good life, Sweetie!" Then she turned around and ran back to me, outraged with me for saying that to her.