As each conductor picks up a coupon, they will punch that coupon to "cancel" the coupon. Some will punch all the way through.
to the hard copy, which the passenger keeps.
On Amtrak book tickets, their is a spot for each conductor to punch, but its so small an area that very few do it, since they now see so few book tickets.

Reggie, I assume you hand write Air Line ticket stock? How about typing them.
Thats what I do, having been "grandfathered" as a agent doing rail ticketing prior to Amtrak, I still use Amtrak type ticket stock, and type most of the tickets and this solves the problem of going through so many copies.

Thats what Amtrak ticket offices once did before printers. In fact thats the first thing that Amtrak purchased new for the San Bernaridno office, was two new manual typewriters for tickets.