I think there are two aspects, and a concern.
First, the technical. If your friend didnít give notice to the Post Office until the new people moved in it is highly likely the new peopleís ISP is doing a house move and has placed an order to take over the line. In which case the PO will not be able to place a Cease Order on the line. Openreach will not accept orders on a circuit when there is an outstanding order awaiting completion.
I expect that is the reason exchange work is required. A physical move off TalkTalkís equipment.
Second, wrt the account, if your friend didnít give notice in time, thatís their problem. If they did, then it becomes a commercial dispute. The PO may need to keep the account open due to the way their system works, but should not be charging past the end of the notice period.
The concern is that the PO or TalkTalk might manage to place a cease order on the circuit after it has been taken over, when closing your friendís account. That used to be possible, but may not be these days.
My broadband basic info/help site - www.robertos.me.uk.
Domains, site and mail hosting - Tsohost
Connection - AAISP Home::1 80/20. 200GB. Sync 75808/13984Kbps @ 600m. BQMs - IPv4