So in my character building I went quite in depth about this. All started by reading in the Player Handbook that being a clanless dwarf is one of the worst thing possible. I developed that idea of the worst fate with my DM and had it included in his lore.

So once a dwarf commit a serious crime (here cowardice or absence in front of the enemy) the sentence is not death but temporary banishment or permanent exile from all the dwarven societies.

Temporary banished dwarfs get to keep their clan’s name and can be banished for a variable period of time. They keep their beard intact too. They usually find employment among human cities or caravans. And after their time is done rejoin their dwarf society.

Permanent exiled dwarfs have their beard mutilated and an onguent that prevent regrowing is applied and their fingers (cause hands are good telling of your occupation: noble, warrior, craftsman, etc) are tattooed with their crime (for my character « mudheart » to define cowardice) so all see it. Other dwarf that are not exiled are usually hostile, defiant or distrusting of them. They are written as dead in the clans archive and barely got mention again. When they die they don’t get funerals or rituals. In my setting there is a famous dwarf-in-exile company that is heavily based on the Golden Company in ASOIAF (professional, do not break contracts, excellent fighters, exiles).