Generally speaking there is limited scope to what happens. Generally, the house is not responsible for damage done by cheaters, and they really don't have a right to say confiscate chips or cash to redistribute them to other players. A private game on the other hand has about any remedy they choose, and have chosen various remedies up to, and including homicide.
lets talk about what remedy a licensed casino has. Like I said they cannot withhold chips, they cannot confiscate cash on their own. They do however have options.
If the problem is during a hand, the hand can be declared dead. Minor infractions such as to many or to few cards, that are obvious just result in a dead hand. With more serious things the hand may also be declared dead and there is no claim to the pot for the cheater, and thus the pot is won by the usual determinations between remaining players. The floor person may try other things like splitting the pot etc. but they really have no authority beyond the scope of the pot on the table. Indeed unless someone is pressing charges, they have to cash out the player, they can't keep the players chips or cash.
Other infractions do not carry the dead hand penalty such as table talk that is against the rules. Sooner or later though the casino may tell the player that they are no longer welcome to play. The player may have been doing something that arguably effected outcome on one or many hands but there really is no recourse as far the money goes. Whatever it is. Some casinos have a policy of not offering any remedy for a hand that is done unless the complaint was bought up during the hand.
Now the player may have been caught with something really severe and obvious like holding out cards using a mechanical device. The player is arrested and goes out in handcuffs, leaving a big pile of uncashed chips at the table. The casino or the arresting agency is going to escrow those, put them into evidence or whatever. The players do not have any claim to these chips as far as the arresting agency or casino go. The players may have claim but that is realm of civil law and not criminal law.
So if you want some of that cash your going to need to sue somebody. It is not going to be the casino, they have no more liability for a cheaters damage then the local police have for items lost in a robbery. It is going to be the cheater you need to take to court, and good luck with that, even if you win your not likely to ever collect.
In tournaments the casino has, usually as part of the agreement, a right to disqualify a player, without the player being able to receive a refund on buy in. I think they pick up the disqualified players stack. If the player was disqualified when they were in the money, the disqualified player does not collect, and payout may need to be adjusted for players that have already placed. It is also possible for a cheating incident to come to light after the player has finished the tournament. Then readjusting may become a big problem and subject to all kinds of things which may work out in all kinds of different ways.
Online it is different. and I think out of the scope of what your asking.