"Hi, I'm calling from Bank of America about your debit card ending in XXXX. We've noticed some suspicious activity. Did you make a purchase for $200 at SomeOutlandishlyExpensiveStore? Oops, I need to verify your identity first? Can you give me your SSN?"
There you have two pieces of not-very-public information from the leak, and some bait to incite a little bit of panic, which might impede their judgement enough that they won't be too suspicious.
Something along those lines. Someone more creative could craft a better message.
Aside from being helpful for phishing, leaking the last 4 is enough for the issuer to pull the card, which is a major annoyance if you have other things billed to that card that will now all need to be updated.
Our financial and business systems are such a house of cards; it’s ridiculous identity and account management is such a utter disaster.