That's money that used to float in the US economy that no longer does.
My mind says that US dollars EVENTUALLY have to be spent here.......it is just a matter of time. Maybe I am looking at this too simply but I am willing to be convinced otherwise.
You are correct. These dollars are like checks we write to pay these immigrants. If they come back here and are spent, hurray!!! If they never come back here then we got their services and they never cashed the check, hurray!!!