Each part of the engine would be assessed at each overhaul. While, in theory, you could overhaul forever, you'd probably not have a single piece of the original engine after a handful of overhauls.

Also, just saying "overhauled" really doesn't mean that they took the engine apart, and replaced every wear item with a zero time, brand new part. I could actually take one apart, measure all the components, find them all "within tolerance", and for the price of labor, maybe some gaskets, and maybe some new oil, call it an overhauled engine.

Caveat Emptor