Dow said the family was "really annoyed" the change wasn't carried across to his son's account, which was attached, and that the library did not contact him or his wife.
"When you sign up to the library the adult takes on the risk of the child losing the book," he told the Herald.
Auckland Council's general manager of libraries and information Mirla Edmundson said a member of the council's debt management team spoke to Ryan's mother about the issue yesterday.
"We have closed the account with BayCorp after being made aware of issues with the family's email and an error in recording a change of address," Edmundson said.
"Ryan's mother has also agreed to go to the library to settle the replacement cost."
She would pay $50 for the lost book.
Under the terms and conditions of Auckland Libraries membership, the services of a debt collection agency may be used to recover outstanding debts and related costs.
Edmundson said memberships held by those under the age of 18 were guaranteed by a parent or guardian.
"In the event of any debts, the parent or guardian is contacted, not the customer who is under 18," she said.
"It is our policy to promote and encourage access to our collections and services."
Council acknowledged the frustration caused by this experience, she said, and hoped the Dow family would continue to use the service offered by Auckland Library.
But Dow said he wasn't confident the issue had been resolved in a way that would prevent it happening again to others.
"After this, to be fair we are cancelling our library cards," he said.
"We are just not going to deal with the library, which is a sad thing"
He was concerned the messages were all addressed to his son, and said it would have been awful if an email addressed to him, had reached him first.
"I hate to think how he would feel."
Dow and his wife had not told the teenager about what had happened until they resolved it with the library, not wanting to upset him.
Dow said the response they initially received was "patronising" and sounded as if the person was reading off a script.
Auckland Libraries agreed to pull it back but only after the family told them they were going to the media, he said.