Nine times out of ten when your faction dies out it's game over. Occasionally, certain conditions permitting, instead of this occurring a civil war may break out. This is caused by your having generals married into the royalty (you had married your princesses to your own generals) or you have generals with Royal blood that were still when the king died.
Personally I always try to create some strong individuals with links to the royalty. When the faction leader dies and his heir succeeds to the throne, the faction leader's brothers usually drop out of succession (the "uncles" you may hear mentioned on occasions). These men can be both an asset and a major problem in that they can be very disloyal to the new faction leader and on occasions lead a civil war against him. They can be an asset as they provide you with an extended Royal line that can help to guarantee your faction's survival. When these men additionally drop from succession you can do a number of things with them:
i) Ignore them.
ii) Disband their units to save on support costs, especially if they're vice ridden useless cowards with 2 loyalty and pathetic stats. In this case it's best to use their units to merge into others that need topping up and then disband what's left. You could also use him as some training for your spies.
iii) You can give them an administrative title to boost their loyalty and other stats.
iv) If they have good acumen they can be given governorship of a province to improve loyalty in particular - and sometimes other stats.
v) They can now be married to your princesses without gaining the Secret Incest/Incest vice - to improve loyalty and more firmly attach them to the royal line.
The first and second points are self explanatory, the next few points can be combined and need some further explanation. The main issue with generals, even those that were previously heirs is that they die of old age (if you're playing MTW v1.x ignore this bit). This means that though a man can be of royal blood and/or married to a princess, when he dies, even though he is replaced by a general of identical stats, vices and virtues, he loses his royal connections and royal bride. The loyalty increasing effects of marrying the princess remain, but the marriage itself does not (signified by the ring icon disappearing). At this point you may want to marry this new man again to another princess, though if you have another finer general he may make a better candidate. The problem is that, not really knowing a general's age, you have no idea if the man you've just married your 15 year old daughter to is in fact 75 years old and could die the next year. This is why you need to keep a constant watch on such generals if your royal line is getting a bit thin. You should marry your princesses to them to improve their loyalty and give them governorship. I regularly demote governors and hand their jobs over to newer more fitting candidates. If I find a group of newly demoted "uncles" (ex heirs) I will very often award titles to them if they're suitable.
The moral of this is: Don't hand your princesses over to other factions, there is very little to be gained from this and they are better used at home.
:bow: