They will give you a receipt when you buy the card that has the card number on it. If you should lose the card, they would be able to look it up from the card number on the receipt and determine the balance. I am just guessing, but I would think they would cancel the lost card and replace it with a new one with the remaining balance amount. If you do not have a receipt, there would be no way for them to look the card up. It does not have a name associated with it.
WDW Gift Cards are like cash. You need to be very careful with them.