Ask a Social Security Question, Get an Answer ASAP!
I realize you have a question about social security. My goal is to help you better understand your options.
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Since you are a resident of one of the countries with which the United States has a Social Security (Totalization) Agreement, your payments will continue as long as you are a resident of an International Social Security (Totalization) Agreement Country.
So yes, even if you give up your greencard you can still continue to draw your US Social Security benefit
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