Why do fingers of your hands and legs become numb when you are asleep?

Yes that can Happen. I have Rheumatoid arthritis and this brought about a situation that led me to suffer from a condition known as carpel tunnel syndrome. this is the median nerve being restricted as a result of inflammation in the carpel tunnel (the middle part of the hand leading up to the wrist) this causes numbness and can lead to excruciating pain in all the fingers side from part of the ring finger and the pinkie. If you are finding problems with numb or tingling fingers get it seen to as it will damage both the muscles around those fingers and the median nerve if it is not fixed.