They don't by default, but they can completely close an account. When they politely refuse, tell them your debit card and checks have been lost and need to be canceled. The bank is on the hook for charges to a debit card that has been reported lost, so it solves the problem of recurring charges to the debit card.
I had reported the card lost which is why it was canceled for 2 months before I closed the account. However, reoccurring charges setup before that point are transitioned into direct bank drafts and continue after that point. As to closing the account, they teller said "it's closed" what are the magic words to say after that?
Send a letter by certified mail to the bank informing them that Mr T. Eller confirmed that the account is closed and that any additional fees, costs whatever are not your responsibility any more?
In that case they either have to react or, if they dream up some fantasy fees later, you have at least something in writing (and maybe grounds for a complaint about fraud with the DAs office) ?
I'm amazed with what US banks can get away:
Selling your private data to some sleazy marketing organization, unless you opt out? A criminal offense here
Charging more the 15% annual interest on any credit granted (including cards)? A criminal offense here
Threatening you because some scumbag used your "pre-approved credit card" scamogram (for which you never asked) to defraud you? They'd be laughed out of court
While I don't believe that it should be the governments role to protect consumers from their own stupidity it should crack down hard on this sort of outright fraud. Good faith is a basis of contract law and contracts designed to defraud one party should be outright illegal (and are actually unenforceable in a lot of countries)
