It will not have an effect on Bitcoins' supply because the supply of Bitcoins will just be the same. Imagine a gold being converted to fiat. The gold supply is still there and in fact remains the same. Just that you have fiat in exchange for value of the gold you once held.
We are even the ones that fixed the value based on how we have perceived it and as long as bitcoin remains valuable and useful, there is no way everyone would want to dump what they are holding. Even if at all we have only one person buying and decide to buy everything from everyone's hand in the world, bitcoin will still have a value for him. But really, this is something that cannot happen, so it is really not worth imagining.this will really affect the sharp decline in prices, this process is long and just seems to be an outrageous one 
It is really something that cannot happen. Unless bitcoin becomes extremely worthless that no one is willing to buy is when we will see such crazy dump. Even if everyone decides to drop all they have, we have to understand that it is at least one person that is buying all of them, so at the end, everyone cannot dump their bitcoin for fiat.We cannot say with surety that what would be the future of digital currencies but yes it is not possible in near future that whole of the coins would get converted into the fiats.