I remember having one... It had no ground wire... Thinking about it now, I'm really surprised I never got electrocuted or that it didn't catch on fire, it was really flimsy.
Electric blankets aren't intended to be used while you are in the bed. Your own body heat can keep the bed warm and they're dangerous to run while sleeping. Their intended purpose is to warm the bed before your own body is in there to do the work. It avoids the first few minutes of sheet shock when jumping into a cold bed before your body heat catches up to the task.
(I always had trouble washing them properly though)