I support the idea that working to abate the causes of crime are more productive than punishing criminals, criminalizing contraband or, worse, trying to control honest folks. I believe most folks are morally good and generally responsible. I see self-defense as the most basic and personal individual right.
I think the folks who invented the term "gun-control" have done a great disservice to the country. I disagree that laws will be effective in changing the behavior of those determined to commit violent crimes. I see the primary purpose of criminal law as serving as a criteria to be used in determining guilt at a trial. Yes, the law serves as a guide for society but I believe laws fall short of any effectiveness as controls. I see safety campaigns as generally more productive than criminalizing items into being contraband.
For sure there are many responsibilities in the world today. Owning anything dangerous carries some extra responsibilities. Many jurisdictions have trigger lock laws to keep your 7 year olds from shooting your 4 year olds. Some folks use a lock box or safe for the same reason.
To the case in point, the only way law enforcement has of determining if a gun recovered through a buy back program is stolen is if its serial number has been reported stolen by the owner. IMO reporting your gun stolen is the responsible thing to do. The buy back staff would be entering the serial numbers to determine if the .38 revolver or 9 milli being turned in is on the stolen list. That's the determining factor to decide if the person should get $200 or $500.
Once the town has possession it seems to me that, barring any precluding circumstances, the right thing is to return it to its owner. Not every stolen gun was stolen because the owner was careless.
(After a background check, etc.)
In short, I don't think you should be treated as irresponsible (too irresponsible to own a gun) simply because you've had one stolen.