When carried out by people deliberately, the practice you refer to -- scoping out the casino floor for lost or abandoned cash, credits, or TITO vouchers -- is known as "silver mining" and is a common source of income for the city's more enterprising homeless, like the character named "Steve" in best-seller Beneath the Neon, who claims to be able to "spot a penny on a machine from 100 yards." He and his girlfriend make between $50 and $100 on an average night from "abandoned" money; they once found $900 unclaimed on a slot machine.
In practice, it often boils down to "finders, keepers," but as to whether or not the practice is actually legal, or what the potential penalties might be, that varies from jurisdiction to jurisdiction and can depend both on the local unclaimed property laws and on the attitude of the individual establishment.
For example, we've read cases of casino staff pointing out abandoned credits on a machine to a different player as a friendly gesture, when their original owner had obviously long-since departed. On the other hand, while researching this answer we read an account from a man whose elderly father found a $100 winning voucher, told security, received no instruction to the contrary, and so went ahead and played it, only to find himself being unceremoniously summoned to a back room by a different member of security, escorted off the property, and told not to return. In Las Vegas, where the problem of homelessness is deep and silver mining is rife, its exponents are not welcome, and can expect to be ejected if caught in the act.
According to a study published last year, it's been estimated that Nevada's casinos could actually bring in as much as an additional $50 million per year just from uncashed payout tickets. On the strength of those findings, Las Vegas Democrat William Horne introduced Assembly Bill 219 in an attempt to have uncashed tickets declared to be unclaimed property, which legally is owned by the state. According to the bill, after the appropriate length of time for the rightful owner to come forward has elapsed (in this instance, three months), the winnings would revert to state coffers.
In spite of strong opposition from the casinos, Horne's bill was passed, meaning that as of July 1, 2011, 75% of the value of unclaimed winnings reverts to the state of Nevada; the casino's share of the bounty has now been cut to just 25%.
That's the long-winded way of saying that, whatever the unclaimed property kaw might be in the jurisdiction where you're playing, abandoned winnings are legally either the property of the casino or of the state. One thing that's clear is that they're not yours and you play or cash them at your peril.
As to the rules affecting found chips or cash, it's been awhile (10/31/2005) since we last investigated that particular can of worms, and if you check out the answer im the Archives, you'll see that the answer there was far from clearcut and varied significantly from property to property. We choose to leave it up to your individual consciences to determine the correct way to proceed.
