To expand on the banking scenario: If you get a call about a stolen/lost credit card don't call the number back (or use a number the caller provides.)

Instead lookup the fraud/accounts contact number for the bank and call them yourself. - aka start the interaction with known good information

Unfortunately there's a scam for that,apparently. The scam caller tells the victim to call their bank, but doesn't hang up. The victim hangs up, calls the bank, the scammer is still on the line.

If you're concerned about that, wait a minute. I can't find any discussion of the scam online, but I would hazard a guess that this isn't really an attack vector these days.

It happened to an old lady in switzerland recently - she didn't hang up, the scammer just got quiet after saying he would hang up so she could call the police, and then had someone else answer the lady when she assumed she was talking to the police.

how is this allowed to be a thing?

The telco's themselves should be held legally responsible for the fraud in these cases.

If I hang up a phone, I expect that to be the end of it, period. Yes, that includes landlines.

..and for those who might not be comfortable trying to find this information on the internet, it's almost always listed on your [credit/debit/atm/etc] card itself.

As mjevans says above, it's fine if they tell you there's a problem, but you should never try to solve that problem over the phone based on a call by a stranger.

Unless you know exactly what you're doing, what you should do in the case of any over-the-phone problem like that, is first contact someone you trust and knows what they're doing. Your own bank, an expert of your choosing (and not chosen by the stranger on the phone), or a knowledgeable friend or family member.

Never trust the stranger on the phone.