I also use my slow cooker on low overnight. If I use a pot on the stove, I'll put my electric oven on "1" for overnight, but let it simmer at "3" during the day.
With an actual flame, I'd be more cautious. I know plenty of Jewish families who keep a low flame on over Shabbos to keep food warm, with a "blech" covering the flame and then the pots on top of the blech. Blech is the Yiddish word for this large metal sheet that goes over the stove on Shabbos, the nicer ones are specially made for this purpose and are insulated. There are some families who only use a blech if they have an electric stove, but blechs have been around for hundreds of years so plenty of people have used them with flames! Traditionally cholent (stew made on Friday to eat at lunchtime on Saturday) was made on the stove and kept warm on the blech; I personally use my slow cooker for cholent.
What I'm not sure about is exactly how high to leave the flame, or how to keep the stock from boiling out if you don't have something to diffuse the heat source.