An exchange Bitcoin (or any crypto) address belongs to the exchange, not to you, as it is them who control the matching private key. If the exchange closes you cannot do anything with this address.

When you send Bitcoin to an exchange receiving address, what matters to you is that this entry is recorded in their internal (centralised) database, which is what you see in your account when you log in. From that point on, anything can happen to your receiving address, what matters is that it won't impact your records in their internal database; your posessions become strictly what is entered in their database.

I really recommend not leaving crypto or Bitcoin at any exchange, for many reasons; centralisation is one of these reasons.