As a professional FanBelt Inspector, and knowing nothing of these LCS's nor the auction,,just what's been posted,,I can say only this:

The 'stolen gun registry' in the USA would be NCIC,,GunINQ File. It's only accessed by L/E.
Firearms are entered by any L/E Agency only after a proper report has been filed by the owner who must show some sort of ownership proof.
They can be entered as 'stolen' or as 'lost' firearm.

The entry stays in NCIC forever.
The entry can only be removed (recovered) or modified (added info) by the agency that entered it originaly.

Someone at the auction knew enough to suspect the gun(s) were in the NCIC file.
A L/E agency had to be called in to 'run' the numbers in NCIC (the file only searches by ser#,,all other data for comparison only).

When the 'hit' came up, the agency that originally entered it into the system back in the 80's had to be contacted to verify it was still active.
Obviously it was,,and those guns will go back to that agency.

They may be nothing more than have been listed as 'lost'
(misplaced,,it happens quite often).
An original report will be on file with the agency reporting giving them the owner, circumstances, last known location, ect.
The report # is often listed right on the NCIC entry so it's available years later as in this case.
The agency will do a followup from there with this info and any new info on where the guns have been since. As always all possible angles are looked at,,theft and even insurance fraud.

If listed as stolen originally, then the original CR# from the agency will likely be on the NCIC hit. It will be used to come up with the actual report.
On it will be the crime and circumstances surrounding the theft (burglary, robbery, auto theft/GL, ect), suspects if any, names, phone#'s, ect.
Any followup will be done by the originating agency from there
including any insurance claim payout/possible fraud.

I'd guess they'll sit for a while in a Property Clerk's closet.