Users with status unsubscribe can't subscribe again

If a user unsubscribe, and get the status of being unsubscribe, if they try to subscribe again using the forms on the site there will only be a text saying "registration failed" due to their email still being in the system. Is there a way to let the user sign up again using the forms? Or as an alternative if the subscriber unsubscribe their account gets deleted automatically from the system?