And the sad part is, and this is just my opinion, it could be different in other places and depend on certain circumstances of the specific crime as to whether it leads to an arrest or recovery of the firearm but if your gun is stolen, or your entire collection of guns is stolen, it's probably going to be low on the list of priorities and the "investigation" is typically limited to the extent that they will take down any information, serials, models, photos, etc and just wait for them to turn up in crime scenes, traffic stops, searches, etc... and even then they probably just go into an evidence room and sit. Not sure if there is a centralized database of guns that can be traced back to the report filer with serial numbers (if provided). I remember a thread I started a while back about whether people log and inventory their firearms by serials. I still haven't done that but need to.
I think in most cases, once it's gone, it's gone so protect it, lock it up and keep your home and valuables safe.