[Alyssia]

I'd still try to talk it out with her completely to see what all she has to say about it, but what she's considering is really dangerous. If she's going to do this the way you're saying her body will begin to consume itself to sustain normal functions. Not to mention it could adversely affect her growth as well as feminine functions.
If she's really looking to lose weight there is no real quick fix for it that won't have consequences. Try and thoroughly explain what she's considering doing and just how much of an impact it would have on her. Maybe if you lay that kind of information on her it will open her eyes.