Retreating Generals

[Liberator]

My generals don't know retreat; they know only victory or death.

And I have a question concerning the latter:
How can I have more generals?

I recently had the realm divide event, hold 19 provinces right now, but I have only 4 generals (Including my Daimyo and 2 of his brothers; no general died in the last decade).
Sometimes there are events that let you enlist a general for 1000 money units.
Is there a way to trigger such an event? Or is it just a random event, not effected by the players actions/ number of provinces???