Proper responsibility lies on both sides of the process of gun ownership. First, the entire process needs to be consolidated. Background checking should be made sufficiently streamlined to be able to be completed within hours or maybe days, not weeks. Second, the government needs to make registration and tracking of gun ownership convenient. A system of independent registrars needs to be established. They can be hired to handle the registration process AT gun shows (and gun shows required to employ these people) with gun show registration being given priority processing, which should enable a background check in under an hour.
Those independent registrars should also be available for hire at reasonable fees by private sellers to ensure that the ownership can be properly traced. Other things can be done as well, such as allowing the ATF to keep a computerized ownership database. They currently have to track ownership of a weapon via microfilm records, starting at the manufacturer. The NRA opposes such a database for some unexplained reason. On the ownership side, owners have to be held rigidly responsible for the proper maintenance and storage of their weapons.
They should be forced to have their weapons inspected at regular intervals by a licensed gunsmith, with the weapon repaired before being turned back over to the owner, or retired and destroyed if beyond repair. No more display cabinets. Guns should be kept in a safe at all times, unless the owner is handling or using the weapon (or perhaps on the property the weapon is stored at). A pane of glass and a thin chain are NOT security. However, a $1000 gun safe, with half inch steel walls and a decent combination lock are ample protection to deter most thieves. Additionally, ammunition should be stored safely and separately. Scheduled home inspections should be required to ensure owners meet storage requirements. If they do not, they lose their weapons.