A person was hired as the assistant to the CEO’s assistant 70 days ago. Since then she’s sent emails to top clients with comical errors -?

drafted a brochure the CEO calls a perfect piece of trash (her previous job was graphic designer at an advertising firm), she helps herself to the CEO’s personal snack stash, and I've been blamed once, She tantrums weekly-the office is so small and her voice is so loud, we hear her complain to both her supervisor and the CEO that run the business wrong- they need to do things her way or she cannot function. She yells at them that they have ‘never read’ her resume. She confided to me(I hate that at work) the skill set on her resume is constructed; she once temped at a place that had accounting software on the computer and she printed out some checks with the help of the staff accountant, so she put ‘proficiency at XYZ’ accounting software on her CV. She says the trick is she just has to find the person in the organization who has the skills and get them to do the work for her. Today is the fifth time in 70 days she’s left & ‘never coming back’. We don’t get any work done unless she’s late or storms out early. HR always defers to the CEO. He and his assistant seem unwilling accept her resignation and let her go even though they have to deal with fall out. I like my job a lot. This person is just totally out there. I wouldn't hesitate to say ‘unemployable’. I don’t want to quit. How should I handle the Queen of all Drama? Do I really have to keep my door closed forever?