There was a book published recently on this topic, or very close it. The title is "Burned Bridge", with some subtitle. I'm on mobile right now, so I can't provide a better source. The goal of the book is to examine the formation of that border, to look at who moved in both directions and why, to examine why the border was created and who benefitted from it, and to show that it was not as simple as East restraining desperate people from fleeing to a prosperous West.

I cant say much about other instances, but thanks to one of these immigration crazes, my country(Czech Republic) has pretty substantial Vietnamese minority that has only grown ever since. Im on mobile right now so I wont link to any exact articles, but it was pretty much the case of Czechoslovakian goverment inviting Vietnamese people as "guest workers" and from what I know, it was endorsed by their goverment as well as a part of knowledge and sklil exchange. After fall of the communists, most choose to stay here.