What happens to a used but unregistered AMEX gift card?

(disclaimer: I accept all liabilities that stem from this question and the actions taken)

So, while cleaning out backstage at my local theatre, a person I was helping clean up with spotted a $50 American Express gift card (you know, the one that you give when you don’t want to “restrict” someone but don’t feel like cash). The card was not signed and appeared to be not registered.

However, after checking the balance on the American Express website, I found it was used once and had less than the $50 starting balance. We’re trying to find the owner and will give it back if requested.

My question comes from the “if” of “we couldn’t locate the owner because the card was not registered nor signed”. Would the card be treated similar to lost cash or as a lost credit/debit card?