Would like to share an experience I know for the the situation.

Back to Dec 2010 (a few days before X'mas), I took CX100 from Sydney to Hong Kong. Upon check-in, the ground staff gave me a J boarding pass saying I have been upgraded to Business Class due to "economy is a bit too busy"... while I was happy with what CX has done for me, there was a conversation over the counter next to me which I found interesting (can't remember the precise words):

There were two Y passengers passed their passport to the check-in staff.

Check-in staff: "So you didn't do online-checkin?"
Passenger: "No we didn't."
Check-in staff: "Well, I am sorry but we have oversold in this flight. At this point of time we do not have a seat that we could offer you. Do you mind to take the next flight which is departing at around 10pm?"
Passenger: "Oh no, how could you do this for us? We have to fly to HK in this flight...." blablabla.
Check-in staff: "Well in that case, we would have to transfer you to a Virgin flight that departs at 2:25pm."

... ...

The two Y passengers ended up taking away two VS Y boarding pass and rushed to the gate.

I guess that might be the way how CX handles non-FF Y passengers when a flight is completely oversold?