The only 2 countries they WONT send SS to is North Korea and Cuba.
This is whether you are a citizen or not.
There are certain countries where you have to "Proof of life" yourself after 6 months (at an embassy etc Ukraine Uzbeckistan etc etc).
But if you have "earned your own" Social Security (eg 40 quarters) and are a citizen of these countries
Then you will keep getting paid after 6 months even if you have given up citizenship and are no longer a citizen/resident of the USA.
All the information is here
Or use this tool https://www.ssa.gov/international/payments_outsideUS.html
There is a good article on tax withholdings etc here at https://www.investopedia.com/advisor-network/articles/social-security-benefits-nonus-citizens/ (short answer is they withhold 30% and then you have to file taxes to get some of it back).
Its pretty simple really.