Firstly, a truly dead civ doesn't get a monarch (nor a dwarven caravan, or nobles beyond the mayor, or migrants beyond the second wave). Due to a bug many civs that should be dead are merely struggling, which results in a monarch, etc. It should also be noted that dead civs are culled from the list of civs you can embark as if there is at least one civ that isn't dead (but I recently found that a "struggling" civ that should have been dead was culled as well). I know of only one way to determine if a civ is truly dead on "merely struggling", and that is to embark and look at the "civ" screens "civ" sub screen. If this is completely blank the civ is dead, but if the dwarven civ is listed it isn't. Also note that as soon as another civ is listed on the civ screen the dwarven one appears as well.
I'm aware of only one way to select a monarch, and that's a rather uncertain one. It seems the monarch is chosen at random after a polite discussion among contenders in most cases (save scumming typically give different results). However, if that doesn't happen (and I'm aware of no way to block it, although save scumming might possible get things to play out differently) the expedition leader is selected as the new monarch at the 2 year mark (with a slightly different message), and in that case changing the expedition leader has resulted in the selection of a different dorf as monarch in my single experiment.