I suspect that in a sane world they would just take the gun and let her go after some paperwork is filled out. But this happened during the Obama reality so who knows.
Right before my mom died and was put in hospital we bought tickets and caught a super early flight next morning (first available) and somehow there were a couple 30-30 cartridges in my laptop bag that I have zero idea how they got there.
It was small western airport and they were pretty cool about it but I did get a warning letter from friendly fedgov that next time I would be in trouble.