I don't see a problem with people immigrating, working, and retiring here.
If the people who come from here cant make enough babies then this is a good and natural to see immigration.
Sidenote: all or nothing immigration is not sensible, the question will always be: how much immigration of which kind of immigration. It is of course a balance thing.
There can not be any nation without it having some sort of borders and criteria for who gets citizenship, nations and the rule of law is there to regulate people within nation states.