Thus extra infaltion is created. It is the same situation as if a private bank starts printing its own paper money with no backing. As soon as trust is lost, bitcons are reduced to zero.
It could also be said as soon as trust is lost, gold coins are reduced to zero, well maybe not all the way to zero but the industrial value of gold to mankind is pretty low once you factor out using it for decorations. Gold is probably worth about the same as copper. Gold is natures perfect fiat currency, bitcoin is a pretty good man-made copy that has the benefits of being electronic. Both are 'mined'.