Saving face is on a continuum. In some cultures it’s more important than others. In some it has more impact on day to day lives. Is some cultures it encourages people to take responsibility and resign to “save face for a company or the state” even when it’s not that person’s fault but rather the fault of the position.

So yeah I think the majority of societies practice this to lesser and greater degrees. Some have elaborate customs around it, in others it’s almost imperceptible.