We would need to ignore how destitute the rest of the world would need to be for a superpower to full-on collapse in its entirety. I’m also assuming you mean that there’s zero semblance of order or organized society.

The military would get recalled and leave American bases, strategic territory, and other occupied areas undefended and open to capture. Economies that rely heavily on trade with the US would need to find new trading partners to prevent potential economic collapse and it might not even save them if they can’t get similar enough agreements or pricing. There are countries that also rely heavily on straight US aid, either monetarily or goods, that would collapse themselves or force them to align with whichever country would give them new aid. Global healthcare would dip without the drugs manufactured by the US. No American commodities like oil or food makes prices of those commodities go up everywhere else.

People around the world would be afraid. Whatever you may think of the American government and US politics, the average US citizen/resident is quite removed from the goings on of the federal government. The states on their own have a lot of independence and some would likely survive a collapse in federal leadership, but if federal, state, and local government all collapsed together it would be something serious enough to warrant attention from other countries with similar structure to the US.