As long the player is open to whatever the DM decides their characters history is, or they have collaborated on an outline or even a detailed history the other players just don't know about, that is all fine and can be really fun for everyone.

If they are doing it with no heads up and are not going to play along with whatever the DM decides happened in their past, then no. But when it comes to DnD, I normally let stuff play out and only stop play if something is clearly going poorly, or might make other players more uncomfortable than they are willing to be. I only play with friends, so things rarely end up being anything close to the worst they theoretically could have gone, socially.