I suspect this isn't much of a problem. Dollars owned by foreigners are in the banking system, often kept in New York banks. For example, I've read that payments to the Saudis for their oil are paid by our oil companies to Saudi accounts in New York, so all those billions just stay here, much of the time. The only problem is with dollars that exist, but aren't circulating, such as suitcase money used in the drug trade. If that ever gets totally laundered and enters the legitimate system, there could be a flood of it. But then again, perhaps most of that is in foreign banks -- which in turn maintain large deposits in New York banks too. In other words, don't worry. The money is already here, one way or another.
Cheers