What happens in the case of a paper ticket? Can you really just cancel the reservation (if applicable) over the phone, throw the coupon(s) away and resume your OWE from the next stop(s), just like that, without reissue?

Edited to add: I mean in the special case of an OWE. I have done the above lots of time with 'normal' paper tickets, and the airlines didn't care one bit, but never with an OWE.