False.
I work for AT&T.
If you sell the phone and don’t pay off the remaining balance/trade the device in, they bill the rest of the installment payments to the next month bill. So the phone is still paid off as the payments are accelerated to the next month bill.
It will not stop the next person who gets the phone to use it on a network.
Only thing that would stop them is if the original owner never removed their Apple ID. Then the new owner would be asked for the password of the Apple ID the phone was setup under.
Here's my take.
I work for T-Mobile.
We have SO many customers that come in with phones they've purchased through FB, CL, or someone who bought a phone and is selling it to them for "a great price" - especially from Costco. As predicted (never fails), the phone/IMEI is blocked, anywhere from 2 weeks to 2 months later. iPhones, Notes, LG... Here's what I notice, though: the ones selling the phone most likely reported the phone
lost or stolen shortly after selling it, causing an immediate blacklisting.
In this case, if he/she sold the phone to Gamestop, they'd still be getting charged for the phone for the remaining payments, right? That's how it works with us. Take what you sell it for and either finish paying off the phone, or don't - but continue paying the remainder of the financing. It's different than a customer bringing a still-financed device to us from another carrier and us saying we'll pay it off - we do that all the time. My understanding with trade-in offers like Gamestop was that you must own the device. Guess that's not the case.
I think that most would agree that the responsible thing to do in these situations is to pay off the phone - it's not yours untill it's paid off (i.e. financing), remember. This is why our companies have those "upgrade" programs as well, where WE'LL take care of the remaining portion of the balance.
Anything less than that, regardless of intentions, could result in a future customer dealing with a lot of grief unnecessarily.
**NOTE** You may see MANY personal online offers on phones that seem too good to be true, especially with the holidays approaching. They - almost always - are. Be careful. Be smart.