This Movie Urban Legends site discusses her probable anorexia and her neck coverings. There’s no good evidence she had anything wrong with her neck for long periods and there are many pictures of her barenecked.
She was naturally skinny and had a skinny mother and grandmother from other things I read. And dancers have fantastically toned bodies. She was 5’4" and probably under 100 pounds, maybe under 90 for some of her career. She might have corset-trained, too, or they could have just forced her into one for shooting.