The sending of emails is not dependent on the status of an issue.
For Company Managed projects email notifications are specified in the Notification Scheme. That scheme defines the issue events for which emails will be sent (i.e. Status change, Comment added, other updates, etc.) and to whom each of those events will send a notification (i.e. Reporter, Assignee, Watcher, Project Lead).
Additionally Automation Rules can be used to send emails to people.
Why do you think the assignee should not be getting these notifications? Is the assignee getting a notification that is not accounted for through the Notification Scheme or Automation Rules?
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