Punkin, this is just a very sad story. It all does make sense though. It seems your sister has had some form of an eating disorder for a long time. They are very difficult to treat from what I have seen. Sometimes people get obsessed with certain foods and they cannot seem to let them go. I have a family member who is focued on bread and margarine. They know margarine is not healthy, because they have talked about it, but they continue to consume large amounts of it, along with bread everyday. It's like a drug to them. They have given it up for periods of time, but always go back to it. Without therapy, I'm not sure what the answer is.
Can your sister get dental implants? I've read of special plans on tv that make them affordable. And sometimes dental schools will allow you to get on a list and they provide the service free as part of their training of dentists. Just an idea. Still, it looks like your sister could get a good amount of nutrition from nutritional shakes, soft food, etc. until she can get teeth.
I wish you all the best.