I've seen many, many rescued dogs this age make incredible transformations....but it takes time. Some recover better than others. All of them I've known have ended up bonding very, very deeply with their people.
Make every single interaction with her about building her trust in you and her self-confidence. Praise every act of bravery, no matter how small. With one of my worst cases, the day the dog tentatively pulled at a dishrag while I was drying dishes was huge -- he was trying to tug. What would be an obnoxious behavior in a normal pup was incredible progress for this one. Celebrate those moments of progress with the dog!
I agree re training. I've seen training radically transform dogs like this about week 3 or 4 into a novice course, when all of the sudden they realize they know the right thing to do, and the world is predictable. In one of mine, there was a magical moment when his face lit up, the posture of the dog changed and the head came up, the ears that had been flat popped up, the stance squared and the noble dog inside him came out to meet me for the first time. It was glorious--and life-changing for this dog.
I'd add this though: interview trainers to make sure you choose someone who understands that rehabilitation is the real goal, and skills are just a means to that end. For a dog like this, the training method has to be very, very positive. If the trainer is used to using prong collars or other heavy corrections, he or she needs to be capable of ditching those and adjusting techniques to suit this dog--good ones can do that, but the skill set is very different than training a "hard" dog. Clicker training would be fabulous for a dog like this.
Be very careful also about doing too much, too fast in terms of socialization. Your job is to know where her "shut down" line is. Never take her past that line. The line will move farther and farther out, but if you try to take her everywhere and do everything too quickly, it will be counter-productive. Baby steps. If she can walk down the driveway, awesome. Next week she might walk down one or two houses and then return. Maybe in a month you can go a whole block. Etc.