The number of guns stolen each year is between 200,000 and 500,000 and we know that enormous percentage of guns used by criminals were obtained illegally.
It is obvious that there is an all-too-easy linkage between lawful gun ownership and guns ending up in criminals' hands.
There are two, and only two, places that we can interrupt this chain of lawfully bought-stolen used in a crime. Either we make it much harder to buy a gun in the first place, or we disincentivize the purchase.
There's another; do a much better job of disincentivizing illegal activity. Overt felonious murder (cases where even suggesting self-defense or other "justifiable" usage would have the whole courtroom burst into laughter) should result in an immediate death sentence. Convicted violent felons possessing firearms should be prosecuted roughly along the lines of what is now the case for attempted murder.
It really comes down to the idea that the crushing majority of firearm owners have no business carrying the onus for that minority of criminals. If anything the onus placed on violent criminals is far too light.