I forwarded this one to Brian, who is a former gaming regulator, and currently a casino manager. Here is what he said,
The casino would not know that someone was in the country illegally. If he had a valid passport, the jackpot would be honored. The illegal may not know this, be scared or they may not have a valid ID to show. Whenever someone wins $1,200 or more, ID is required for tax purposes. If someone doesn’t have his ID, the jackpot would be held in the cage waiting for them to claim it. In most cases, the person has legitimately forgotten their ID; however, sometimes you run into a problem, such as a minor who was gaming. If he doesn’t claim it, the money has to be added back into revenue because the deduction (jackpot) was never paid or there are abandoned property rules that prevail. Also, like the U.S., most countries tax worldwide income. To that end, the U.S. has tax treaties with several countries to withhold or notify the respective governments of monies won in the U.S. so Uncle Sam always gets his cut.