This could potentially happen (though it is unlikely).
If this has been asked before, feel free to say below. This is self moderated to cut down on spam.
Bitcoin can't overtake the total market cap of fiat unless governments abandon it. The reason fiat has value is that it is mandated legal tender for the world.
So I guess to answer your theoretical question if bitcoin overtakes the market cap of fiat it implies more than half the worlds economy has abandoned fiat.