The stories make it pretty clear that if you want to leave you can just leave (maybe slightly different if you are an SC operative)? Similarly the Culture is fairly open minded about immigration to the Culture - but they worry about that looking like a form of colonialism so it's not like they advertise it...

That's certainly true - the minds obviously do care what their humans want, and go to some effort to help them get it. I just thought the idea that "pets can't leave" was funny and not entirely true, given some of the experiences I've had with them.