Yes, but not without mod usage.
The EA way: The sims all around your actively being played household exist for your sims' convenience, amusement, and sometimes to provide mating material. They are expendable and will rotate out (get culled) with new ones arriving periodically when EA's version of story progression is working as it should which, for many if not most players, it just doesn't after a while. Even the ones you don't want to have this happen to, even those previously played by the player or who are best friends or blood related are subject to such removal. It will happen with greater frequency in worlds that the game itself thinks are overpopulated or out of balance demographically, but after a generation or three the game gets confused and it happens rampantly to many players anyway.
The NRaas way: NRaas StoryProgression shuts down emigration (culling) totally by default. No one leaves town unless they die, are homeless NPCs who much more volatile, or the player removes them from the game. If the player wants some degree of automated emigration so that things continue to feel fresh around their actively being played households and the world doesn't end up stagnating with everyone related to each other after a few generations, that can be arranged for within the mod's settings and exemptions can be set for households that should not be touched by this process.
AwesomeMod, our "friendly competitor" for modded story progression, has different ways to manage immigration and emigration but with some work can provide similar effects.