there's a thing called a limit switch in your plenum or heat exchanger. if the air temp in the plenum/heat exchanger gets to hot, the limit switch cuts the furnace off.
if the limit switch fails and you have a fire, well, it's a regular old fire and the damage will be what it is depending on this and that. maybe the house burns down or maybe the damage is limited to smoke in the mechanical closet.
no matter how you look at it, fires arent good.