Well, you can do that too! If a faction has a significantly smaller amount of generals (really, family members), than cities, they will get the option of adopting a captain or other leader every turn. If they only have one stack of troops, there's only one place this individual can turn up.

If you want to kill a faction off by assassination, you'll need to use several assassins and spies, locate all living family members, and take them all out in a single turn. If you fail, the survivors will adopt more people into the family to fill out their family tree, and you'll have to do it all over next turn.