I ask this because this is actually happening right now and would like to know if there is any historical precedent. I cant imagine how this wouldn't create a blackhole effect where most all of "manipulated monies" flow in a mostly unidirectional path into the "sound currency".
Well I cannot personally think of an example of the exact scenario you suppose. The first thing to consider is that whilst economies do sometimes suffer from runaway inflation, if the currency remains legal tender then people will still tend to use it - in the German hyperinflation people did not start using gold widely, for example, it would have been too inconvenient.
A more apt example might be a system where a non-legal tender currency was quickly abandoned as it was deemed worthless, that of the Confederate States Dollar. The analogy is again wanting because in addition to being abandoned because people quickly realised that not only was the CSA funding itself by printing money, but the problem became worse when it seemed that the Confederate government itself might cease to exist.
However, currency crises in general have similar effects, and they are not pretty. The first problem is that people who have their money in anything but equities suffer greatly - if your money is in a bank account, or any fixed-income investments, it will effectively become worthless. Such trends tend to hit middle-income and older people hardest. Yet it seems usually currency crises are politically/socially more manageable than the deep depressions which fixed-supply currencies tend to make more common.
I'm not sure how much that would apply here - you are talking about a currency which has managed to originate organically and is not legal tender. All the things people talk about in this context, like Gresham's law, don't really apply.
But for the above to happen people would have to abandon fiat money very quickly. If this were to happen the financial system would find it difficult to cope; people would suddenly be withdrawing vast amounts of tender and converting it to a currency that the orthodox financial system is not used to dealing with. The result would presumably be a severe liquidity crisis.
A world in which everyone used virtual currencies (as I assume that's what we're referring to here) of various values and issued by various people, which were usually fixed in value would probably look like the unregulated currency/banking system of the United States prior to the Civil War. This would mean sudden financial panics and erratic prices (no steady deflation/inflation) as the currency supply would be solely related to the fixed supply of currency and the policies of banks, not the macroeconomic situation.
Sorry, this has digressed into economics, but I'm not sure if history has much to say there - perhaps if anyone knows about what happened with early paper money in China and the fate of the Jiaozi/Chao currencies. Also it might be useful to look at how more recently in Latin America in the 1990s, dollarisation (people switching to using the dollar rather than national currencies) affected the economy.
The evidence is though that currencies come and go - witness the break up of the Latin Monetary Union, the various countries which have had to replace their currency because of currency instability (Israel, Hungary, Germany, Turkey etc.). But usually it is from one government-created currency to another, hence usually the reasons are as much socio-political as economic.
I cannot think of an instance when people abandoned a currency en masse for a new one without it being a managed process.
Are you asking if there is a historical example of people rushing to use a currency that was appreciating in value (possibly one with fixed supply) at a time when most other major currencies were suffering from inflation (ones which were essentially fiat money, I assumed, given your reference to bankrupt sovereigns)?
Just want to confirm because I think we're all familiar with the argument about fiat currencies (gold fans, bitcoin etc.), just wanted to make sure that's what you were talking about.