The JIRA documentation for deactivating users says,
Will not receive any email notifications from JIRA, even if they continue to remain the assignee, reporter, or watchers of issues.
However, when users have been marked as inactive they are not excluded from emails sent to groups via the 'Send Email' function from within the Administration screens.
Suggest that inactive users are excluded, or administrator is given the option to exclude inactive users from email
Remove user from all groups. This would prevent JIRA from sending emails to this user when sending email to a group.