It varies, but basically the following is true: You won't get kicked out of the game, death is an intrinsic part of the game and it would be sad to let the death of your regent be the defining factor of player defeat or victory. Shortest game ever!
In case your regent dies there are a couple of possibilities. First and foremost is the prepared version. You get a temple to cast the investiture spell on your chosen heir and once your regent either decides to abdicate or dies, your bloodline and control of holdings and provinces pass to the heir.
Then there's "Land's Choice", this happens when a regent dies, no heir is apparent and no pretender attempts to win the throne by force. The land chooses someone, which is usually a member of your regents familly and almost allways someone who fits the alignment of the nation.
Third is the classic "disintegrate into chaos" version. Usually due to a massive conflict over who's to rule - like it happened in Mhoried. This happens whenever there is imbalance in your realm, conflict with the temples or the like.
In any case, I would definitely urge you to look at the
http://www.ruinsofempire.twilightpeaks.net/ page. It has a link to the Yahoo group and various downloads, most importantly the rulebook, RoE Domain Rules. It's a long and complicated read, but absolutely worth it if you want to master the game.
