Overnight cooking: Is sous-vide safer than electrical oven?
On top of the stove the issue is boiling dry. At that point the temperature can rise almost unchecked. This will result in unpleasant fumes at best, flames at worst. Even in the latter case, because you should be using a fairly tight fitting lid, everything should be contained, but I wouldn't rely on that.

The oven is different. Once the pot is up to boiling point you can set an oven temperature of just over 100&deg;C. In the unlikely event of boiling dry, the contents still won't exceed that temperature - no burning. Like you I assume an electric oven.

Using a sous vide circulator you'll actually struggle to get the inner pot hot enough - you generally want a gentle simmer for broth/stock. The outer pot will loose a lot to evaporation even if it never boils.

I'd have more confidence in the oven, but if you're shopping there's one more option - a slow cooker. Making stock is trivial: put in bones (and any veg etc.); pour over boiling water; leave on high for a few hours or low for up to a couple of days; strain. I normally use low overnight for chicken stock with onion, celery, &amp; herbs. These are specifically designed to run for long periods unattended without boiling dry (as the power input is low and the lid fits tightly).