Some simple facts that should help you:
In CRM 4.0, if you disable a user, all Workflows that they own will no longer run.
In CRM 2011, 2013, if you disable a user, then the Workflows that they own will continue to run. Edit: In CRM Online (2013, O365 platform), if you take away a user's licence, their workflows will all fail. Not tested in other environments.
If you remove some privileges from a user who owns a triggered Workflow (or one called as a child of a triggered workflow), then some or all of the actions the Workflow tries to perform might fail if they require those privileges.
If you remove all the Security Roles from a user who owns a triggered Workflow, then it will fail at the first step.
If you remove all the roles from a user who owns a Workflow that is run on demand, this should have no impact since the workflow is run in the context of another user.
Hope this helps.
Adam Vero, Microsoft Certified Trainer | Microsoft Community Contributor 2011
UK CRM Guru Blog