Thanks to everyone for the advice. Luckily the issue hasn't come up yet between us but I'm unsure of how much longer my advice will last. Sooner or later she might start asking me if she can stay here and I know what to do now.
I do feel a little bit selfish about the whole deal. The economic reasons are quite minor, and my parents are great people and will do anything they can to accomodate someone in need, as will I. I just can't help thinking that she's not 'in need' at all. If she'd just open her eyes she could see, perhaps not that she's got it great, but that her home environment is certainly not unbearable, and in many ways downright great (free food, internet, petrol, accomodation, etc.).
My answer will be no, and my reason will be that there are better ways to deal with her feelings. I'll help her in other ways, but she can't stay here.
Thanks everyone