Extinction of surnames happens when a family has no more sons. Sons usually carry the surname of the family, and when there are no more sons, that surname disappears. Think of it like a game; once all the pieces of the game have been taken off the table, the game is over and can't be played anymore. In the same way, when there are no more sons in a family, the surname is like a game piece that has been taken off the table and won't be used anymore.