Ah, well...not exactly. When someone leaves, their Pokemon obviously can't go back with them. They don't belong in your homeworld and since you lose your memories of this place once you go home and pick up right back where you left off, a bunch of random monsters would complicate things.

[Probably to preserve the sanctity of the timeline or something? Fuck if he knows. He knows how all this works by now but not why it works the way it does.]

In any case, the Pokemon left behind either find their way to other trainers or disappear into the wild. Typically, they find their way to their trainer's friends but this isn't always the case.