(This happens with domestic buyers too but the problem of huge empty investment properties seems to have come along with foreign investment?)
Not quite.
A wealthy citizen of a 3rd world country has used the fact that he can pollute and treat his staff like slaves - to make tons of money.
He can then go to another country wherein surpluses are spread more evenly - buy up property - and start to dominate those people economically as well.
One could make the cases that 'you cannot buy homes in our country unless you're a citizen of a country with similar rules regarding externalities like the environment, human rights' etc..
Because a lot of this money is coming from countries where all sorts of externalizations are made.
Same thing for manufacturing: we 'stop hiring' in locale A and go to 'locale B' where we can pollute and have slaves. You can't really look at it solely from the context of locale A.
For the same reason different nations have separate currencies, I think we need to separate domicile policy.
How does this reason translate to housing policy?
Housing - and capital inflows/outflows - are primary drivers of inflation! (FYI I know housing is generally not included in inflation targets, but it really should be because it's where inflation can effectively be hidden).
Ergo - strongly related to the issue at hand.
Put simpler: those who come from countries with a different currency should not be able to buy residential property. :)
The parent post may've meant to imply race.
cultural factors may play a role, of course. quality of life is better when you have more things in common with your surroundings. this is about preferences, not perceived superiority though. at the very least you'd want your kids to have a common language with their classmates though.