Such requests should be honored as quickly as possible. Ideally, anyone that has requested to be removed from a marketing email program should not get any additional mail after the removal request was made. The length of time allowed for suppression to occur varies by law and country, so ‘immediately’ is the best practice.
A general unsubscribe request applies to all marketing and non-transactional mail **from your company**regardless of what list or division the mail is coming from. After an unsubscribe request is received, all mail to that recipient must cease. The sole exception is if the recipient is clearly notified of what mail they can expect to continue to receive and given the ability to unsubscribe from all mail, such as through an account preference center.
Furthermore, creating a “new” marketing segment and adding previously unsubscribed addresses to it is considered sending unsolicited bulk email (i.e. spam) in Spamhaus policy and may violate laws in certain areas.