And with servants, assistants, and toadies, they'll run the risk of being overrun in a inside revolt.
One of the books in the Jerry Ahern series "The Survivalist" dealt with just such a scenario. When a post-apocalypsian bunker is opened, it turns out that the current "rulers" are descendants of hired help who revolted and took over the bunker.
It seems pretty obvious that the employers in the bunker, cut off from the world of police and ICE, and unable to force fired employees out of the bunker, would have little or no leverage over the hired help. If only there were a way to surreptitiously install nanny cams in these bunkers...
I like post apocalyptic stuff, so I’ll put that book on the list.