If a user has unsubscribed, his email address will automatically be placed on a blocking list (aka "blacklist") in your database. This is to make sure phpList will never send any message to that email address again.
If a user wants to subscribe again, after having unsubscribed, he will see a message explaining he has been placed on that blocking list and can request manual intervention by the phpList administrator to remove him from the 'blacklist'.
You should find an option to manually remove a user from the blacklist in Admin main page > Users > click on the blacklisted user > History > click on "Remove User from Blacklist".