It can break down sitting on the shelf in the original container having never been opened. Cooking oil (vegetable) or shortening should be nearly flavorless and odorless. There may be a slightly butter scent or taste but nothing unpleasant. When vegetable oils oxidize (breakdown) the start to smell and taste rancid.
Cooking oil breaks down if left on top of the stove. However, the stove has to be hot for this to happen since the oil will have reached its smoking point. This refers to the temperature at which cooking oil or fat begins to break down. The quality of the oil is also taken into consideration for this to be effective.