I know about the Weimar Republic's mark, the Yuan war funding, and the more recent Yugoslavian dinar. But are there any cases of a catastrophic currency failure caused by hyperdeflation in a similar manner?
In a hyperinflation, people try to hold goods instead of money because the money will be worth less next week.
In a period of deflation, people try to hold onto money instead of goods for the opposite reason. however this isn't as practical for most people because they NEED goods like food and shelter. For this reason, HyperDEflation is historically rare and rates of price decrease of much more than 10% are unusual and almost never last long.
The result of any significant deflation is typically that people and businesses reduce real economic activity (acquisition of goods) to try and stockpile cash or reduce debts. For this reason, deflation is thought by modern economics to go in tandem with a depression, and the 1930s Great Depression is the leading example of this. Whether a deflation causes a depression, is caused by a depression, (or both!) is a more complicated question. Mainstream modern monetary and economic theory tends to say "both" and a severe episode of deflation, especially if unexpected like a stock market crash or a series of bank runs is thought to produce a recession or depression. This is still an area of active theoretical debate among economists, although central banks greatly fear deflation and act according to mainstream theory linking deflation to recessions..
TL:DR HyperDeflation doesn't really exist and Deflation destroys economic activity, not currency values.
Edit: fixed a lot of awful wording.