Hi Steph
You are free to request a paper-based assessment, but they are unlikely to grant one without a doctor's letter confirming that it would cause you 'overwhelming psychological distress' to have a telephone or a face to face assessment. Be warned even then the DWP and/or the assessment services sometimes ignore such requests. I've only ever heard of two people get paper-based without a medical professional's back up.
If you have a paper-based assessment are you chances improved or disadvantaged? it's almost impossible to say in the current circumstances. Paper-based assessments are great in there is no stress or intrusive questions from an assessor, however, they have a disadvantage in that there is no opportunity to clarify any questions the assessor may have or say something you have forgotten on the form.
It is vitally important that your friend provides as much information as possible, as they will not have the opportunity to attend a face-to-face assessment. Examples of information they should think about including would be medical reports, care plans, statements from family and friends who know about their disability and how it affects them. Also details of changes in medication and treatment if this shows that their condition has worsened, or they have not responded positively to their previous medication or treatment.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems