Digital currencies by nature is volatile so obviously, when a country moved out from fiat and gets on board with cryptocurrencies then their monetary system will be unstable. This is unless they will create their own digital currency and will be centralized and be regulated by the government. That way, they will avoid volatility and sustain its stability. However, this is just a digital version of fiat.

On the other hand, I doubt this event will happen. Phasing out fiat is not a good way to go, for now.