BT Phone Rental

macman

I'd consider it 'unreasonable' not to actually read a bill in 16 years. That's about 64 bills? Nothing you have said indicates that your mother (or more, recently, you) is incapable of doing that. Elderly does not automatically mean 'incapable'.
Your mother may have had a car 16 years ago. If that had an auto-renewing insurance policy, would you blame the insurer for billing her for it even if she no longer had the car, but hadn't told them?

Buzby

I hate being an apologist for BT, but the charge for the corded phone included full replacement when it was reported faulty. Initially, this was a swap to a working version (refurb) but later became a new replacement. The onus remains with the customer (or family members) to ensure that the best deal is being provided.

It was a major failing that there was no earlier intervention - but BT would still be held liable to repair/replace as required and that was what the charge was for. There is very little they could reasonably do - arbitrarily ceasing cover would disadvantage the consumer.