If the U.S. were a smaller country, "completion of the cycle" would mean a combination of drastic currency devaluation, rise in that country's interest rates and imposition of "austerity measures" (to use the ugly World Bank phrase).

Things probably cannot actually turn out that way, because too much of the existing international trade structure depends on the value of the dollar staying within a range. Instead I expect to see some combination of the following:

The dollar tied to some sort of "basket of currency," with specific exchange rates subject to periodic renegotiation;

One or more black markets coming into existence, involving both international trade and movement of goods inside the US, especially energy-related goods such as petroleum products;

US interest rates rising significantly;

Several new and mostly secret bilateral agreements made between the US and other countries, involving both trade and military matters such as arms sales. Such agreements might impel the US to reduce its military presence in some areas, while increasing its presence in others;

A slowdown of US imports of crude oil and petroleum products. The price of other imported goods should also rise.

The other "normal" alternative would be war in some form or other. But war between the US and the rest of the world is simply not going to happen, mainly because it would cost too much.