It means someone was successful even though they really did not do anything to deserve the success. "no fault of your/their own" is an idiom which means that something happened to you (and it could be good or bad) even though you did nothing to cause the event. Someone knocks on your front door and gives you a million dollars. "Through no fault of her own, Angela is rich!" You were standing on the sidewalk waiting for the light to change so that you could cross the street, when suddenly a car jumps the curb and hits you. "Angela was standing on the sidewalk minding her own business when, through no fault of her own, a car hit her."