No, that's not normal for it to come COMPLETELY off. Check the base of the nail that was lost: did it fall off or was it torn? What do the other nails look like? Are any of them loose?
If the other nails seem fine then it's possible that his nail was ripped off by something. However it could also be caused by an autoimmune disease called Symmetrical Lupoid Onychodystrophy (SLO). Take your dog to the vet for a check and mention this condition to the vet if you think this may be the case with your dog. Greyhounds, Rottweilers, German Shepherds and Giant Schnauzers are affected by SLO more than any other breeds, but others can get it.
http://www.grassmereanimalhospital.com/S ...
It's not totally impossible for a claw to break off sometimes. Inspect the point where the claw came off, and if it isn't bleeding the dog will be fine. The claw may just have been weak from an injury to it when the base was forming. My dog runs on concrete floors and he has had claws separate on his hind paws before.
Sadly what probably happened is he got it caught on something and tore it off. Just check it every day until it's healed to make sure it doesn't get an infection. If it does take him to the vet for antibiotics.
not normal vet now