Depends on what the change is and when it happens.
The ticket will be changed to accommodate the original booking. If it is just a number change with no route change, they will just move you to the new number.
For example, if you were booked on QF2 LHR-SYD and they changed the stop over point from DXB back to SIN. Nothing would change. You'd stay on QF2. If you had however booked LHR-DXB on QF2 and QF no longer stopped in DXB, you'd be moved to one of the BA flights.

In the case of the always changing AA flights...
If you booked for example BOS-SLC, and that route (where ever they happened to have the stopover point) was no longer operating, they would rebook you with a connection at one of AAs many hubs, so you might now have BOS-DFW-SLC. If the ticket was maxed out with the 16 segment e-ticket limit, they would tend to wait until the first few flights have been taken before making the changes, eg they'd wait until you have 12 flights left before changing it.
If that can't happen, such as the flight being first, they would get creative and find ways around the e-ticket limits.

The last LONE4 I took had NRT-MEL at the end. QF canned that flight shortly after ticketing, but before departure. I had 16 sectors and it had been issued as an e-ticket (this was just as the paper tickets were in the last stages of being phased out). I was rerouted NRT-SYD-MEL and reissued with a paper ticket with 17 sectors.
After departure that trip, there were civil issues in BKK (one of their riot/protest/government change messes a few years ago) with travel warnings and waivers out. Due to the issues, I opted to forgo the stop in BKK and go right to SIN. While in MAD, I emailed the travel agent at home who made the changes and created a new e-ticket with the remaining flights and the changes to fly FCO-LHR-SIN instead of FCO-LHR-BKK-SIN.