I think existing liability law could probably handle that well enough... if you have something stolen and were negligent about storage you might have some liability.
That said id be willing to explore it.
My only concern there is
1) the rules for storage cant be prohibitive such as requiring a safe which many people wont have money or access to
2) the user should be allowed to keep it unlocked and without a trigger lock at a minimum while they are home ao in the case of a home invasion thry have quick access to it
One might expect that if you keep a gun at home youd take reasonable precautions if you left town such as security camera or somethibg maybe. As long as the two concerns above are properly balanced i would consider more discussion about ways we could better address this.