I did have my debit card details stolen a few years ago. The first I knew about it was a text message from my bank telling me they’ve frozen my account and I need to call the phone number printed on the back of my card ASAP. Spoke to a chap in the fraud department, we went through a list of recent transactions, flagged two charity donations I didn’t recognise (apparently that’s a common way for fraudsters to figure out whether your card is valid), and the bank gave me a new account, new card, new everything.

(incidentally, your bank never needs you to move your money to a “safe” account, they already have your money, they do that for you)