I just tested this, and there is more than one fault behavior. I created two users: Designer and Controller. I created a workflow that gets an explicit user assignment and then sends an email using the value of a global workflow variable as the recipient email address.
1. If the workflow user exists, is active, and the email address is valid, then the workflow task is assigned to the workflow user and the email recipient receives the email.
2. When I deactivate the workflow user, the workflow task faults and is assigned to Controller and is visible to Controller as a workflow task awaiting the next known good activity. It's also viewable in the workflow task monitor. The task is not accessible by Designer in any view.
3. When I enter a bogus email for the global workflow variable, then the workflow faults and is assigned to Designer and is visible to Designer as a workflow task in error activity "General error" with prompts to Retry, Continue, or Stop. Additionally, it is not viewable by Controller in the workflow task monitor.