Japan is the leader of robotics technology for a reason - a lot of eggs are going into that basket.
I don't really think failing societies will do what is necessary to reverse the trends - the opposite actually. With decline comes uncertainty and fear and so those that people that remain will entrench themselves and try to prevent "outsiders" from taking advantage of their own population decline.
Like, say if China ends up half of its current housing available in 70 years - opening up to foreigners, really anyone, to buy them and immigrate on the cheap would be smart... but that would mean a society that has just experienced an incredible trauma then turns around to watch half of their world be taken over be optimistic, eager, productive 1st generation immigrants - it is unlikely Han Chinese 3000+ year old culture emerges from such an experience without much change... I'm not sure that would be acceptable to some countries.
I think a lot of places will go down with the ship so to say, or at least want to. I've no doubt half empty county's will attract attention.