Yes - you do not have a contractual right to AOL a line. That is simply not part of the contract. YOU signed the contract when you bought the subsidized phone and Verizon can hold you to the contract for the length of the contract term - Verizon does not have to let you AOL a line to someone else.
Currently Verizon does allow AOLs if the person to whom you want to AOL the line has acceptable credit in Verizon's eyes. But Verizon can stop allowing AOLs at any time and they absolutely can refuse to AOL a line with UDP intact.
However if the person accepting the line assumed liability believing the UDP would remain intact because the rep either told them it would or they specifically stated they only wanted to assume liability on the line if the UDP would survive the AOL, then THEY have a contract issue with Verizon.
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This is true - there are no provisions in any of the paperwork that would allow Verizon to re-transfer the contract back to you w/o your consent.
This is only true if the person accepting the line stated that they would only take the line if the UDP remained intact or if the rep stated that the UDP would remain intact. But even then, it is a matter of proof. If the AOL calls are recorded then you have that proof. Idk if they are or not. But even if they aren't, you could subpoena the rep and put them under oath and you would testify under oath also then it would be a matter of credibility of witnesses. Obviously that would all cost a lot of money - a lot more than the $350 etf. It would cost Verizon money too and if they thought you were serious about pursuing it they may very well cancel the contract w/o the etf.
But if I AOLed a UDP line and the UDP didn't survive the AOL, I would ask for a the recording of the call and otherwise pursue the name of the rep, etc. to let Verizon know I was serious about getting UDP back. I would let them know they either needed to give me the UDP back or let me out of the contract w/o the etf b/c.