First of all, breathe. A very important thing!!!
Now, lets go over this a little...
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The only little girl (in a cage by herself) has something sticking out of her pouch. It looks like skin, and is not wet or bloody
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What exactly does this look like?
sounds more like her pouch may be inverted? It is good that it is not bloody. That is a big plus. It would only be wet if the joeys were just going into the pouch and they make their trail for them.
How old or about how old is she?
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Do people not think about this sort of thing?!?!
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Some people dont think about it or think because they are family they wont breed. Others do it intentionally.
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Why would someone just leave them all together like that!
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Unfortunately, some people just dont have the money or the thought to seperate them. You stated they were rescues so possibly the previous owners just couldnt afford or they truly didnt *know* any better. You would be surprised at how many will tell you that it is ok for gliders to breed with each other even though related.
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Is it going to kill her. I know she will probably kill her babies.
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Will it kill her? No, more than likey not. Never heard of one dying due to this. Will she kill the joeys? That is possible if there is something wrong with them that she senses. However, she may just have a healthy joey. Just because it is possible they inbred really does not mean you will wind up with a deformed joey.
I would recommend getting her a cage mate though if she does have joeys in her pouch. She will need some help taking care of them if they make it. A neutered male would be the best.
I hope this helps ease your mind a little. I know how scary this thought can be. Pics would be a big help if you can get some for us.