Do just what you would do if you didn't know this person, as if they were someone on this board, say. Continue to give them what support you can anonymously. After all, you don't know my real name, or Whoever's, or Kaybee's, right? That wouldn't keep you from offering support to me, or having me give support to you.

And if they are looking to you to support them in more than just their fight with the medical condition, then you might gently suggest RL support groups, or counseling, or whatever is appropriate.