I manually reassign incidents based on workload to others which takes care of the incidents. Then I change the user type from analyst to End User. I then adjust roles and remove groups. AD takes care of the rest as they can't log on when the account is disabled. I have never tried to demote a user without reassigning all incidents but I really doubt that there would be any errors or messages when the user is demoted if incidents are still assigned. Since no links will break there should be no issues. If an incident is assigned to a group it will still be assigned to that group, the GUID's did not change.
It would be pretty easy to create a query where the Current Assigned Analyst is a specific user. I would do all of this before demoting the user to an end user.