Unfortunately, that doesn't happen. That Vietnamese producer might use those dollars to purchase something from a German producer. The German producer might use the dollars to purchase something from a Japanese producer. People willingly accept those dollars because, ultimately, they represent a claim on something in America. You might ask, "OK, Williams, I go along with what you're saying so far, but if that's true, how come we're running a large balance of payments deficit?"
Do a Web search for major foreign holders of U.S. Treasury securities. As of June 2003, foreign holdings of U.S. Treasury bonds totaled $1.347 trillion. Japan is the largest holder with $441 billion, followed by England with $122 billion and Mainland China with $122 billion. Thus, dollars are coming back to America, in this case to help sponsor Congress's profligate spending. Also, we mustn't forget that foreigners also use their dollars on Wall Street to purchase stocks, bonds and other financial instruments. All the nonsense we hear about balance of payments deficit ignores the fact that there are two types of accounts: a goods and services account and a capital account. Any imbalance in the goods and services account is offset by the capital account (stocks and bonds).
The bottom line is that free trade, while it might mean painful adjustments for the few, benefits immensely the many through cheaper prices and wider choice.