Its also worth looking into as when you end a contract with a company, the DD doesn't necessarily get cancelled at the bank, the company just stops making the request. This to me is rather sketchy as it means any glitch and they could request a rogue payment without you even knowing until its come out.
As such, I've taken to always manually cancelling the DD on Internet banking after the last payment has been taken.
That "new details being shared" with credit/debit cards is also awfully sketchy as a business I hadn't been an active customer with for about a decade got hacked, long after the card I used expired. Somehow some scammer still was able to make transactions with the details they acquired. Not sure if it was due to the automatic updating of card details, but I guess it might be if it was incorrectly flagged as a regular payment despite being idle.