I had this happen on a round trip ticket (agent did pull 2 flight coupons on the previous flight, the airline actually found it as part of the lost ticket processing). I had to file the form and pay the fee for a lost ticket (this was available from the airline ticket counter) and my original ticket was re-issued. As I had to travel the day that I discovered the missing coupon, I had to buy a replacement ticket. This was then refunded (even though it had been used) when I got the lost ticket re-issued and then returned it. Apparently you can't exchange or refund a lost ticket, so it was a rather cumbersome process and took 90 days.
But for a OWE ticket can't you just re-issue it and forget that there is a lost segment coupon? This is cheaper than the lost ticket fee and much easier to do. For a re-issue I've never seen them actually look at the remaining coupons, all that counts is that the new reissue is within the rules and the base ticket stock (ticket number) matches (I think).