Excellent question because the most common reason for FIAT to exist is by force and requirement of an ongoing ruling government of that country. Its quite possible for everyone to choose an alternative to that currency if they are able, some currencies are more reliable then others so thats natural some will prefer that quality and just what they already know.
The foundation of the Dollar was based around what existed prior to it which is the Spanish empire and its use of gold. So USA did start off with gold but has become now a political currency relying on the status quo and its heavily favourable as the most recognisable long term currency though others have been more favoured in the last hundred years.
FIAT becomes worthless when its not used by anyone for any purpose. The most obvious case would be where the value of the paper exceeds the stated value, people have used currency as wall paper and fuel for fires before because it was most valuable in that way after losing any previous value. The main answer is about a competitive market which always exists, people will trade gold, barter food and others items and take the inefficiency in those trades if paper FIAT is more awkward and unreliable to store over night.
Seriously speaking. Fiat will never be worthless once government is still have power. But once a country was taken over by other country thru war then most probably the fiat of that country will be worthless.
FIAT can become worthless while a government continues. No person or collective can defy science and alter the dynamics which can cause the failure of a currency, they can apply force but in the end the bullets used may be more expensive then all the use left in the money created. The currency must serve a task, provide utility or it becomes a burden not a benefit or with any value.
The relationship between fiat currency and a country cannot be separated because the legitimacy of the government that makes fiat currency can be used as a legal payment tool in a country or at the international level. Many factors cause the value of fiat currency to become worthless. The main reason is because the value contained in money is not backed up by gold. paper money material does not represent the value of money, in contrast to gold coins whose intrinsic value is the same as the value of currency.
The simple analogy is as follows, gold provides a guaranteed value to the currency, no one doubts gold as a precious precious metal. With the existence of a gold guarantee when issuing / printing money, the value will be more stable because there is trust. Human nature for material problems is what can be felt by the five senses.
Fiat money becomes worthless when the market or society loses confidence in a country. The stronger the value of its currency, the country must also be strong. When the government of a country prints money to overcome economic problems, other countries will doubt the capabilities of the government and that country will ultimately lead to the loss of confidence in the government which will inevitably make the value of the currency low.