I was worried too about leaving the stock pot unattended
I was worried too about leaving my stock overnight or leaving the house while the stove was on.
The first time was in a temporary rental on one of those ghastly glass-top stoves. I bought a really cheap thin metaled 20 quart pot and was worried the whole time I'd return to the apartment greeted by fire trucks as my cheap pot melted onto the stove and set off the alarms. Not so.
Second time was on my wonderful gas stove. Same cheap pot but my goodness I couldn't believe how much better the stock turned out with the even heating only gas can give you.
Oh, and I did it one more time on that glass top, I left it over night while we slept, or at least the family slept--I kept waking up and running into the kitchen to make sure it didn't melt and set the place ablaze.
I'd say, don't worry about leaving the pot if you have to leave, just be sure it's at the correct simmer and why waste the energy it takes to make a few cups when for the same amount of energy you use you could make a few quarts at a time.
I buy my chicken parts in bulk, like 20lbs of backs necks and feet. If I could get a 100 quart pot and it would actually fit on my stove, I'd be in stock heaven.
I freeze them in 1 cup zip locks laying flat on the shelf.
Hope this helps.