Is a person who got green card through asylum status allowed to visit his home country where he fled ? I have not been home in 10 years and need to visit my ailing mother.

I would suspect (but I'm not a lawyer) that you'd better have a good reason why you now believe that it is safe for you to return to the country you supposedly fled in fear for your life.

Isn't it amazing how a country that one flees in apparent fear for life and limb suddenly becomes "safe" upon receipt of a green card?