As a responsible seller, you are responsible for the buyer having in their hands what you advertised and they paid for. I always include shipping and insurance in my sales. Insurance can be paid for or you can be self insured, but in either case the claim with the carrier is between the shipper and the carrier, not the buyer.
Another way of dealing is where the buyer has the shipper ship the item using the buyer’s account number with the carrier – aka FOB – in this case, once the item is in the carrier’s hands it is the buyer’s responsibility that it arrive safely or deal with the carrier himself.
This avoids the situation you are in entirely, before it happens, because what you describe here happens all too often.
If I have a dispute, the first thing I do is refund the buyer’s money and have the item and packaging picked up by the carrier.
Buyer beware if you did not work this out ahead of time.