When your father dies, do you become a bastard? or only kids that are born without a father can be bastards?

All children have fathers (except for clones). However, some mothers don't have husbands, and THEIR children are bastards. It used to be a big deal in the Middle Ages. Bastards were not allowed to inherit unless legally adopted by their fathers, and bastards were not allowed to enter a church, therefore they could not marry legally.