Actually they often do not really abandon the currency, they just issue a new dollar that removes a bunch of orders of magnitude from the dollars.

http://en.wikipedia.org/wiki/Hyper_inflation#Currency

Users (not issuers) abandon the currency as a currency until the measures are taken to assure that some measure of value stability will be restored.

Doing what amounts to a a "reverse split" on the currency is a measure issuers take to get the unit value of currency to a usable value.