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have traded the Bitcoin to Fiat and withdraw it to your account, so what will the exchange do after you have already withdrawn the money to your account before they later found out that the coins was tainted?
How is this possible, OP? As soon as you deposit funds to the exchange, they are automatically checked by AML. If the exchange has any questions, your account is blocked until the circumstances are clarified. You must provide the sources of these bitcoins, be it a statement or a screenshot; in addition, the exchange will definitely ask you to provide documents. After that, you may be offered to withdraw your "dirty" bitcoins if you convince the support of your innocence, or the bitcoins are simply frozen, although I think this is completely unfair.
What to do next with your already marked in history, not quite clean bitcoins, you will decide on your own. However, it is highly unlikely that you will be able to successfully exchange your bitcoins elsewhere.