I had 10 day tickets starting around March 5th or so, 2020. After using 5 days worth of tickets, on the Thursday morning before the parks closed down due to covid I tapped into DHS and went straight to guest relations and said I was ending my vacation due, in part, to safety concerns. All five in my party got 5 day complementary hoppers.
Not only that, I augured that I wanted 3 complementary fastpasses for each day of my next trip and the cast member at DHS said sure...so my next trip (last March) I had 3 recovery anytime Lightning Lane passes for each day of the trip.
My feeling is that conversation notes are made by just about any cast member that you talk with over the phone. If they promise you anything, it will be recorded (and you can tell them to make a note on your file), and with enough persistence you are able to hold them to whatever they say/promise.
That was a very unique situation
Used tickets are not normally extended and had the parks not been closing due to a pandemic, I don't expect you would have gotten your tickets extended either.
People can't just decide to leave 5 days early and extend their tickets
If someone is there and an event occurs like a pandemic or hurricane, then sure, you can probably get some sort of compensation for unused park days.
But if you have to leave of your own accord, then not likely.
And what that CM told OP was flat out wrong. Many, many CM give guests wrong info. Sadly, you can claim it was told to you all you want. Wrong is wrong. Just because the CM said it, it won't make it fact. Not all the time. They simply make too many mistakes.
Now, I feel there is zero reason for a CM who works in ticketing to not know these things but that doesn't change the fact that they don't. They are not trained properly or given proper resources to gain the info they need. As someone who used to work a help desk such as this, there is software out there that operates off key words. If Disney used it, all the ticket desk CM need to do is enter key words such as tickets, unused, expiration, and the rules associated with it all come up and they can all read the same info to callers. No reason for any to ever give out the wrong info. That's how help desks normally work. Even those who use remote agents. Leave it to Disney to do something else.