Oh, I see. It is very difficult situation. Yes, a brief acknowledgement of the medical issues, and then a change of subject. Of course, if she is used to getting this attention, you may have to retrain her into accepting a change of subject.
I don't know how your group is facilitated, or if this is a possibility, but one technique to change focus is to have members talk about something that is going right, rather than wrong. Staying positive is important for us all.
As for the emails, simple questions to her such as "how are you addressing your health issues" or "what is the solution for this problem" may help her take some responsibility for herself.
I think if you encourage her to spend less time focused on her ailments and more time on the solution, she will either join the discussion or leave and find another group who plays into her self-pitying behaviors.
As for the enabling behaviors, I would limit any emails that give attention to her eating disorder. If your group focus is fibromyalgia, you may suggest that everyone stay focused on this topic.
I would not spend a lot of time with this issue. You are working on getting yourself healthy, as are the other members of the group. This one appears to be trying to remain unhealthy, and is defocusing you from your own goals.
She will remain sick for as long as she wants. Do not accept responsibility for her behaviors, and do not play into her self pity. Please let me know if you have further quesions.