If an application user that owns business processes is leaving your organization, ownership of those business processes needs to be transferred to another user, otherwise processes owned by that user will stop working after the user has lost all permissions.
To check and see if a user owns business processes:
1. Go to the Admin tab > Security > Application users 2. Find the application user in question and click on their name > then click on Business Process Ownership 3. If they have own any processes, ownership of those will need to be transferred to another user.