Everyone during the 1800's and before had a shotgun, rifle or (before that) a musket over the fire place (loaded) and ready for self defense or simply a place to put it for later use to hunt food.
They probably had zero accidents by doing this because...
1. There kids were taught the dangers of misusing it as well as how to safely handle it.
2. Very young family members and friends of family were smart enough not to handle them because of the strict discipline that would happen if they were caught picking one up.
As for the weapons being stolen...
That was a chance they were willing to take. If stolen, they probably knew who they were and simply hunted them down and retrieved them one way or the other (most of the time without the sheriff getting involved)
No registration, no trace of who owned the weapons were required. Most homes had a weapon and almost ALL of the bad guys knew and avoided breaking in since the owners had access to them at a moments notice.
Oh, for the good ol' days (as Archie would sing) when "girls were girls and men were men"