I’m of similar perception as Brygun; the food will burn, but as long as the fire goes out, it’ll be fine and gets checked as “in cellar” for the daily spoilage check.
You can easily test it by roasting a cut of meat, while standing on cellar, with 3 branches. Leave the cooked cut untouched, add considerably more firewood to the burnt out fire, light it up: if you get note stating it smells like it’s burning soon, you’ll know it’ll burn up.
It does do that elsewhere.
And on the other hand, if you drop any cooked and picked foods, say at your fishing shelter, then roast fresh catch, none of the previously cooked foods, including roasted, will give you the message of burning smell.