How long can you leave a pot of soup or stew on the stove, and not refrigerate it?

I have an uncle that has a stockpot that he calls his mulligan stew pot. It gets replenished with odds and ends, and the occasional adding of beef or chicken stock. It always smells tasty & never spoiled, is he a good cook or is he a nutcase like my grandmom (his mom) & aunts (his sisters) think he is?