ASnakeNeverDies: When a game has multiple endings, there should be no "true ending." The hypothetical sequel should assume all endings were true, and resolve conflicts from there to create a consistent background.
That's a very tall order, but admirable when pulled off.
Mass Effect sort of does this when starting each sequel. Though the particulars of the ending do not vary much. They all have same outcome, but slightly different circumstances about it.
The only game where I personally seen what you describe pulled off to full effect is The Suffering and its sequel, Ties that Bind. The first game has three endings, and the second game has three beginnings. You get the neutral one if you don't have a save from the first game. I think a handful of other games do this as well where they check the previous game's save, but that's a tiny fraction. That's a hell of a good way to handle it, but I can't imagine that being doable with games of any serious variation.
In all of this, I think I can see why developers typically avoid these sorts of situations.