In those extremes, maybe gold and silver would be priceless. Historically in third world countries, hard currencies were utilized in lieu of the local money, typically US dollars, German marks, Swiss francs.
In terms of paper currency yes, they will be. More accurately, paper currency will be worthless.
If you have a local network that’s willing to take gold and/or silver, more than likely in terms of real goods, gold and silver will settle down to a certain value, probably not all that different than what it has been historically.
In severe economic disruption, people may not be willing to take precious metal and will stick to barter if they don’t feel they can exchange gold/silver for goods with the next guy.
Even so, it’s better to not let the value of extra cash waste away. Once you can survive, convert the rest to precious metal and wait for better times.