Let's imagine the entire rest of the world thought that the dollar was worth nothing. Well everyone in the US still needs dollars to pay their taxes, so they'll still want to get their salaries in dollars. Similarly, people will sell stuff in dollars too. Now if someone outside the US wants something that someone in the US produces, they'll be able to get it really cheaply by trading their valuable currency for tons of dollars. They'll do that, buy stuff from the US, and make a huge amount of money. This obviously presents an upward pressure on the dollar's value, until the cost of things from the US more or less balances out.

As long as there's a base of goods/services that can be bought and are priced in dollars, dollars will continue to have value.

Why would the fed need to buy back dollars?