Hi Kevin -
I've run the following experiment on performance activities to answer what status would be assigned and whether notifications would be sent on a closed instance after the due date passes. What I did:
Confirmed that notifications should be sent on or after the due date on the activity (was not on by default)
Created an activity and closed it before its due date
Observed notifications sent on due date and day after
Observed status of the activity on due date and after
Findings:
Activity is showing as 'closed', 'not submitted', and 'overdue' the day after the due date, even though the activity was closed. Note: We are developing a bit of an improvement for this, so that 'closed' and 'not submitted' are the important statuses and 'overdue' is either hidden or reduced in importance
Notifications are not sent for due date reminders once the activity is closed. Note: I didn't try all notifications, just due date reminders.
I hope this helps!
Ashley