Hi! Hope you are doing well!
This is not possible in a Shopify. If the user has placed an order for some address, then it is to this address that the shipment should take place. The fact that the user will change this address in the account does not mean that all old orders or those that are to be delivered are sent to the wrong address. I hope I understood your idea correctly and my answer will be enough for you.
When a user/customer change data, it does not update an email to the ower shop, you just can check it manually currently.
Hope this helps!