2003 Ford Taurus Mysterious Shredded Belt

My car stalled out yesterday, and when we popped the hood, we discovered one of the belts was shredded. This is on a 2003 Ford Taurus, with a 2.4 valve Duratec V6. I know it was not the serpentine belt. The shredded one was on the right(driver's) side of the engine, under a particular cover by itself. I have been told that it is the timing belt, but every place I have tried to find a timing belt for that particular car tells me it doesn't exist, because those cars didn't have a timing belt, but a timing chain. This is definitely not a chain, so I am at a loss as to what belt this is? And how much the part is to replace? Also, previous to the stall out, the car overheated right before I got to work and this was the first time it has ever done this. I checked the antifreeze(after it cooled down, of course) and it was full. I also was bone dry on oil, and I have not had a leak on it ever. I just checked it the previous week, so it shouldn't have been like that.