When the collar has continuous wear-through (ie inside and outside are no longer attached) a shirt gets converted to "septic service". They get hung in a separate closet and don't come back from that. One wear and they're done.
If the collar is only worn through here and there (ie not continuous) I wear it to the museum restoration shop. It's quite likely to get spray paint, grease, oil or a snag there. I patch small tears in long sleeved shirts (using iron on patches - on the inside of course) and wear them to the museum too.