FIAT money is our daily currency which has been existing here for hundreds of years, when crypto currencies like Bitcoin is squeezing their way up to become a world currency and sort. Can they co-exist? If so then what benefits we can get from them, altogether? Not separately.
Nope. Well, there indeed were some examples since 11th century, but the era of domination of fiat money came in 1971 when Nixon decided that backing up dollars with gold should go away forever. The whole name comes from Latin 'fiat' which is like 'let it be/ it should be', so the nature of this infinite money having value because the government says so is revealed. Can cryptos coexist with fiat? Sure, but they'll probably inevitably replace the latter because of many problems the potentially infinite amount of money of a certain currency leads to. Cryptos have a new mechanism that allows to make sure the supply is limited, but at the same time not linked to a specific resource, since too much money is needed already and no resourse could back it all up.