ii) For a non-U.S. person, one or more of the following: A taxpayer identification number; passport number and country of issuance; alien identification card number; or number and country of issuance of any other government-issued document evidencing nationality or residence and bearing a photograph or similar safeguard.
Granted I just quickly skimmed, but it would appear that as long as the person has a tax identification number, which they happily give to the illegals so that they can get a refund of our money, they are covered by the FDIC. And the of the big reasons they send it home is to buy property to return to, so they put the money in the foreign bank to pay the bills. At least this is what the ones I worked with told me.
You literally risk being picked up by ICE for making your claim.