I don't think this can happen to Bitcoin. Of course, people save Bitcoin and spend fiat, but they don't save their Bitcoin because it is "good money"; they do so because it's a good asset.
I've seen situations where a person decides to use old and wrinkled fiat currency and save the freshly printed mint, but those kinds of situations are not significant enough to cause anything to happen.

Demand and supply drive the value of currencies or assets, so as long as there is a demand for Bitcoin, it will always have value. The more people save it, the more the value will rise and that will drive more people to invest in it because they wont want to miss out and this will further drive the value up.