Countries become "un-rich" by running budget deficits, not trade deficits. My country does not pay my rent, or buy my beer.
If the US runs a trade deficit of $1 jillion this year that means it has net doled out $1 jillion of cash (or IOUs) to the rest of the world. What happens if the US keeps that up every year? It has to print out $1 jillion (in IOUs if you must) for each such year to make up for it, doesn’t it?