The vast majority of firearm owners are responsible and law abiding individuals.
Responsible ownership can be demonstrated by obtaining insurance for the firearms they wish to buy or currently own.
Firearm insurance would be for the life of the firearm and would be irrevocable by the owner or the insurance company. The insurance would pay for any (illegal) harm done with the firearm, even if the firearm was stolen, loaned, or sold to a non-responsible third party (i.e., someone without insurance). The insurance would only terminate when the firearm has been destroyed or sold to another responsible person who obtains insurance for that firearm.
Current owners can self-insure all their current firearms.