The exchange don't care for that moment but as soon as the destination wallet report your wallet address for stealing of funds or comprises, they will seize the funds immediately if you haven't used or withdrawal the money and if you have withdraw the money before the report, you account will be suspended with all your information given to law enforcement to track you down, this is the main reason why they ask you to do KYC verification in the first place.

If you are using a centralized exchange to deposit and withdraw funds, try as much as possible to make sure that your funds are clean as possible, if they accept mixed funds which I'm don't they would, mixed your coins before you deposit them to exchanges and if they don’t, don't try it. Rather, make use of decentralized exchanges to swap to other assets and then you can send it after to centralized exchange where you wouldn't have any problem later.