Shaikh Raajihi was asked the following question:
Some people play with their beards sometimes, then some hair falls from it. Is there a sin upon them because of that?
The falling of dead hair does not harm when showering and when making wudu. However, it is necessary for a person not to play [with his beard] deliberately. May Allah facilitate everyone towards his obedience.
[Reference removed since it no longer exists]
Faisal Ibn Abdul Qaadir Ibn Hassan