This happened to my GSD as well when she was younger - she injured her toe twice within one year. Both times - inflammation & cut and just dangling there. Took her to the vet - he said there was nothing to do for a broken toe (if it was broken or bad sprain) but if this toe was to become a problem - it would probably need to be amputated. She was given antibiotics in pill form and spray.
It never happened again. To this day - I do notice that same toe to not sit like the rest of her toes but it never became a problem. This happened 2.5 yrs ago!
If it happens again, go see your vet!