If you think about what fiat is and how it works you'd realize that this is impossible.

Fiats like USD have an unlimited supply so they can not be backed by anything with a finite supply. In fact that is why they stopped the Bretton Woods system a long time ago!
They are currently printing about a trillion dollar every 100 days. How would they continue this if each dollar is supposed to be backed by anything including BTC? They can't stop creating debt either.