In the terms and policies of some centralized exchange, they stated that they don't accept Bitcoins from an untrusted source such as mixers or a wallet that has been flagged, some exchange even stated that they don't accept Bitcoins from casinos.
Anything that has to do with privacy, and they can't track the source of the funds; most exchanges just don't like to deal with that either for regulatory compliance or for whatever reason they might have.
So, if any customer disobeys those rules and send Bitcoin from the mixer or any sources that the exchange doesn't want, they will block the persons account and the customer could lose their coins forever.
If the customer disobeys the exchange rules, then whatever decision that the exchange takes as action, they should be ready to bear it. To use any service, you agree with their terms, which, if you don't, you should not use in the first place.
The exchange are doing so to protect their image too based on the government policies, I guess.
So, when they cease those coins, how sure are we that they will take it to the government?
We only assume, but we can't be too correct because we don't have internal access to the exchange. In cases where money which they don't trust is being deposited into an account either from a casino or mixer, in most cases the best thing for the exchange to do for them to free themselves from being used as money laundering tools is to return the money back to the address which it was deposited from down to the exchange.
Sometimes, after making such deposit, before the exchange detects it, you must have traded the Bitcoin to Fiat and withdraw it to your account, so what will the exchange do after you have already withdrawn the money to your account before they later found out that the coins was tainted?
In cases where it comes from an address that the government has already frowned upon, which they refer to as the tinted coin or tinted address, the exchange will freeze those coins and ask for you to explain their source, which, if they are unsatisfied with your explanation, is the best way to take the law into their hands, which is blocking your account and not allowing you access to anything in that account.
Another thing that just popped in my head now is, what if after you deposited the Bitcoin because you needed some money and wanted to convert the Bitcoin to Fiat, but you later changed your mind and you decided to withdraw back the money to a newly created address, will the casino report that your address to be flagged?
In the case where the person has already withdrawn the money before they realise where it came from, the best thing they will do is flag that account and ask you to explain how you came about the in and out of such coins, which, if you are unable to explain or they are unsatisfied, they will block your account, and that's all.
They can't have access to wherever you withdraw your money to, but if it's a case that warrants investigation, they will forward every single detail of how you converted the coin using their exchange to the right authority, which will give the authorities a clue of where to look and how to track the individual down.