>They are also dying out very quickly and have no immigration to replace dying out people.

I think I get what you mean but keep in mind that Japanese cities are severely overpopulated. Their country is returning to a more normal population level. It's ok to not have Bangladesh levels of overpopulation, and they don't need to be "replaced" by immigration in order to maintain the current population density. Also housing in Japan is not cheap outside of the cities (where no one lives) so your point doesn't really begin in the first place.