My Bela is a former puppy mill mama, about five years old. We had some MAJOR problems to overcome, and still do after five months, but she's coming around.
The two biggest hurdles are the lack of socialization and the unfamiliar noises (both inside and outside the house). The lack of socialization is a relatively easy one to cure, especially if she isn't aggressive. Just take it slow and easy and use trusted, well-socialized dogs to introduce her to the bigger world.
The issues with unfamiliar noises are more problematic. Bela came to us afraid of just about any household noise. Also, she went ballistic over thunder and lightning. Unfortunately, the first month we had her, we had a major thunderstorm every three days, and after about three weeks of this, we had a storm in which a large tree came through the back wall of our second and third bedrooms. She hid under the master bedroom bed for almost three days and could not be persuaded out by any means. I finally just climbed under and dragged her out (probably not the best solution, but it worked). A ThunderShirt and Rescue Remedy (as did the occasional Benadryl) did wonders. After she settled down in general, the extreme fear of thunder has diminished almost completely.
The worst noises for Bela are metallic (i.e. a metallic collar tag against a stainless steel bowl) and dishes (the sound of putting dishes in the dishwasher). It took a lot of observation to figure this out - for instance, I could not for the life of me figure out why she would start to take a bite of food, then look scared and run and refuse to eat. I changed her to a heavy plastic dish and took her collar off, and voila! no problem with eating. The thing with dishes clattering has been a more difficult problem, but has diminished the more comfortable she has become with us and the household routine.
She also had initial issues with her potty routine. She came to us fully (and supposedly reliably) housetrained, but was so upset by the change in routine that she refused to potty AT ALL for the first three days! We had a few accidents for the first couple of weeks, but other than that, she is very reliable for up to 8 hours at a time.
She's very timid sometimes (but is an alpha dog, which is puzzling) and loses confidence very quickly, making training her and keeping her motivated a problem. That, too, has become less pronounced as she begins to relax and become more acclimated to the household routine.
A lot of times, she cannot be persuaded to do anything at all on her own (for example, she simply will not enter the kitchen under any circumstances on her own - even the offer of her favorite treats doesn't sway her). In those cases, I have found that putting her on-leash and gently walking her into the kitchen, and attaching the leash to the pantry door while I am busy in the kitchen has helped. I talk to her constantly during this, and randomly give out treats. It has helped, but not cured the situation.
She also will absolutely not jump up onto the bed or sofa or chairs. This is a big problem for me, as I broke my back several years ago, and cannot lift a 20 pound dog. We are still working on this one, and it seems to terrify her to even try and jump. As her confidence grows, I believe this will disappear as well.
I think the best thing we've done for her is getting another dog. Bela's foster home was full of other Shelties, and though she was noticeably anxious there, she did enjoy the company of other dogs. Her first four and a half months with us, she was an only dog, which probably was good for her as she didn't have to compete for our attention. Two weeks ago, my hubs (unwisely) came home with a little JRT/doxie mix named Gracie. While I had extreme misgivings - Gracie is an exact polar opposite in personality - Bela and Gracie have become the very best of friends. Bela has gone leaps and bounds in progress in the past two weeks, and she doesn't even seem like the same dog. Where Bela was emotionally almost shut completely down before, now she is beginning to see a little bit of the joy in life, and you can see it in her eyes, replacing the pitiful apathy she had before.
All I can say from here is that obstinate love and stubborn patience will ultimately work, as long as there is a spark there to begin with. And with your foster girl being only 11 months old, I think you have an extremely good chance at totally rehabbing her!
Good luck, and my prayers are with you!