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Finders, Keepers is a the premise that when something is abandoned, whoever finds it can claim it. However, defining "abandoned" is legally difficult.
One of the most common uses of "Finders, Keepers" involves shipwrecks. Under international maritime law, for shipwrecks of a certain age, the original owner loses all claim to the cargo. Anyone who finds the wreck can then claim it, and subsequently mount a salvage operation.
Occasionally, in the case of winning lottery tickets, someone else will claim to be the true owner. Assuming that this is true, the possessor of the ticket can claim that the original owner abandoned the ticket, thus laying the groundwork for a "finders, keeper's" claim.