We have daily UPS pickup and delivery and rarely have any issues with them. Horribly badly packed incoming stuff from clients is another matter.
However, it is normal UPS policy to pick up and inspect equipment damaged in shipment. They will want to inspect the shipping carton and packing materials too. A claim may (rightfully) be rejected if the packing material is inadequte. We tell our clients to ship to us packed so that the equipment will survive being kicked down a very long flight of stairs. If the buyer has disposed of the packing material before the unit is inspected, it is likely that a claim will be rejected.
Anyway, since the shipper (you) paid for the insurance on the package, you will be the one that gets reimbursed for the damage or replacement cost. You then reimburse the buyer when the claim is paid. After inspection, the unit will be returned to the shipper (you) generally, unless it can be repaired by simply sending out a replacement part. In our case the most common damage (and rare) is a faceplate corner bent and UPS normally lets the buyer keep the unit while we just send them a new faceplate which with our stuff is easy to replace.
If the unit is totaled, the UPS has the right to keep the piece after essentially paying you for it. Often however they do not exercise that right.
The buyer needs to cooperate with UPS and let them take the piece for inspection. The buyer should take pictures of it, as any further damage caused while in the UPS system must be reimbursed too.
Simply look at it as you sold the unit to UPS assuming the claim goes through and deal with and take care of the buyer accordingly.
Best luck in resolving this.
Regards,
Frank Van Alstine