The answer in general terms is yes. Fiat can, will and has failed. A more nuanced answer now, however, might be, "Is it too big to fail?"
EXAMPLES OF FAILED CURRENCIES
Within the last 75 years, there have been all kinds of fiat currency failures. Five such money crashes include:
—Papiermark, Germany, or the Weimar Republic
In each instance, some elements of too much debt, failure to pay on that debt, and attempts to change monetary systems existed, leading to what ultimately undid them all—lack of confidence in the value or worth of the currency. The worst of them hyperinflated into the billions, and in one case, (Papiermark), the trillions.
MUTUALLY ASSURED ECONOMIC DESTRUCTION
Now, more or less, the countries of the world exist within a global economy, where most are tied to every other in some way. That is why, for instance, markets in the U.S. will get jittery any time China or countries in Europe are having issues. We essentially owe one another's debt in a rather dangerous game of robbing Peter to pay Paul. Governments are running billions to trillions of dollars in debts and deficits, all of which will fall upon the taxpayers of each sovereignty to pay should they ever be called due.
It's likely that this won't happen as long as the central banks responsible for different countries' or regions' economic policy making can continue to hold interest rates down and prop up the failing nations with more loans in exchange for what has been known as 'austerity policies" which are often nothing of the kind.
However, at some point, there will be so much debt and so little capital that not even the interest on the payments can be made. The US alone is well into 20 trillion dollars in debt, with unpaid liabilities exceeding 100 trillion.
And yet, the U.S. isn't likely to be the country that goes down first, unless more changes in its status as the world's reserve currency takes place. Already, countries around the world have been looking at alternatives, including a basket of currencies to replace the U.S. as the reserve currency. Still, the United States is in a position to digitally create money, and as long as that is the case, it can continue to float along.
THE SYSTEM IS FRAGILE
Ironically, what would ultimately cause a nation's fiat currency to fail wouldn't be a spend and keep on spending type of policy as it would be a reversal of that. Any awakening among the populace that some form of trouble is brewing, or that a crash is imminent, could cause a run on the banks as account holders attempt to get what's theirs. In cases of such panic, banks generally close their doors to prevent withdrawals, but now, with the advent of online banking, it could be possible to transfer money out of accounts in one currency and put them into something else to preserve them. Still, the sites could be disabled if such were the case.
In reality, it only takes a percentage of the citizenry of a country to lose confidence in their currency for things to fall. There may be many reasons for that, but the consumer is the one who ultimately decides, and when they do, it will spell disaster for the fiat there, and probably elsewhere, until the cascading effect is felt around the world, plunging us all into the mother of all global depressions.
This potential failing of fiat currencies due to unsound monetary policies, excessive spending and huge debts, is a big reason why cryptocurrencies even exist. The ability to provide a digital currency across all borders and boundaries, one that is not governed by any one public policy, that is not beholden to one individual or entity because of its decentralized nature may ultimately be what saves many from the economic ruin that will come when fiat fails.
Failing is not an if scenario. It is only a matter of when.