Offshore US dollars are generated from thin air by the international offshore banking sector:
The download link here opens a law review article as 97 page pdf:
The United States Fed and Treasury cannot "weaponize the dollar" without a functioning international legal system linked to the government policies of political allies. If the bankers don't obey the court orders, or the orders of the US Treasury, regarding sanctions or judicial orders, then the police take the bankers to jail in some jurisdiction. If there is no police jurisdiction over the criminals, or use of police force or military force against political adversaries, then the dollar are beyond the jurisdiction of US authorities. Trust in the dollar is in the rule of law via the judicial sector and use of police force. But the Sovereign US government exerts the dominant influence through the international government cooperation, commercial customs, and judicial customs.
Joe