EXACTLY! Which is why we should have a resource to verify stolen firearm! Your local LE should be able to say "please call/visit this phone number/website for that information". Of all the stupid, useless, .gov programs we fund that don't accomplish ANYTHING, we can't have one that would actually take stolen firearms off the streets!?
I would like to walk into a gun store with the buyer of my firearm, pay a 10.00 fee (limited to 10.00 by federal regulation), wait for a background check to be done on both parties and for a serial number check to be done on the firearm (stolen/used in committing a crime check), and receive a receipt when done. The receipt can be saved in case that firearm ends up in an investigation.
Because of federal gun regulations that already exist, the above would give me piece of mind. This idea should be OPTIONAL.