Once a member has cancelled their membership or expired, they will not longer appear in Active or Partial results in the Reports view.
You may still wish to periodically contact ex-members, however.
One way to keep track of expired members is to add them to a Group. Although this is, at this stage, a manual process, it enables you to send Group Emails etc to contacts easily.
If the Contact no longer wants to receive emails, they can unsubscribe if they wish.