Your dog is only in danger if he has a bleeding disorder.
Or if the nail becomes infected. Keep an eye on it.When a dog breaks off finger nails off to the point where their veins are showing and bleeding could that kill?
They can't die from a broken nail. It is painful however. I suggest taking him to the vet to have it checked out. They will usually bandage the foot for a few days and send them home with antibiotics.
It is possible that your dog could die if you don't take him to the vet. Please Take Him!!