Let's say your flight is delayed excessively and you miss your connection (on the same PNR or linked). Let's say AA will generally put you on the next AA connection available, and if it is the next day, if your delay was caused, let's say, by weather, you would probably not get a hotel voucher - but you could ask for a chit showing you qualify for the distressed traveler rate.

Let's say your delay is caused by a mechanical problem with the fist aircraft - AA is likely to give you a hotel. Let's say another airline has seats available and an agreement with AA - an agent might follow the "Rule80" (no longer a rule) and endorse your ticket to that other airline.

On the return, let's say your PNRs are not linked, in which case AA could charge you a full walk-up fare and change fee to continue your journey. They probably would not, but they can.

This is all theoretical, of course, as much as your post is.

Let's say you want to learn more about your rights and responsibilities as an American Airlines passenger: read American Airlines' Conditions of Carriage, as well as American Airlines' versions of Rules 80 and 240 for more information.

(Read 'em and weep - they wrote much of it themselves, and IMO are some incredibly self-serving bullbleep - deregulation was an all or nothing series of changes, and the airlines were empowered previously to write themselves their own "tickets" - Warsaw Convention, Hague Protocol, Montreal Accord, Chicago Convention on International Civil Aviation, Rome Convention and Geneva Convention. They kept the elevator and gave us the shaft.)