Again, speaking as myself, not for my company
>Are you able to track balance checks made against card numbers not yet activated?
Yes. Can't get into specifics. Not every card supports balance inquiry though. Not entirely sure how this applies to physical gift cards.
Usually what happens is that someone simply writes down the card number, and waits, and then tries to redeem it. They don't do a balance check.
>Presumably you could also take things back to the level of "store X, you have a serious problem."
We can get down to the register. Fraudsters are sometimes employees. But you can't treat customers like criminals so doing anything about it is hard. These same stores don't seem to mind customer info leaking and credit card data being stolen in the first place.
We sometimes have to replace these cards for consumers, because it's dumb to spend a hundred dollars for a giftcard and it was stolen previously, that's not their fault