Unless its just music
(I didn't know the term, trying to be helpful if others don't)
Depending on implementation, it will either pause or play the old sample where the new one isn't yet but should be.
An xrun typically manifests itself as a (very short) discontinuity or gap in the audio signal. It might sound unpleasant, but there's nothing dangerous about it.
https://www.audioadvice.com/audioquest-nrg-dragon-high-curre...