Without reading anyone elses post first here is what I'd do..

She know you have health issues and that you do NOT need the stress. Little ones, even as sweet as they are will disrupt your life as it is, then she has a problem also... For my health I would say "NO" in a heartbeat. That would be inviting trouble into your house and setting the stage for you to get worse.

Offer to help her find a place to live and even help her set it up if she needs help but invite her into my home.... NO!

I will tell you this. One of mine ran into a bad situation of their own creation and found themselves homeless with 2 kids and asked if he, his wife and kids could move in with me. I told him "NO" and reminded him the situation he was in was one of his own makings and why should I be burdened with his bad decisions.. HOWEVER.... The kids were innocent in all that so I took the kids in and let the adults fiend for themselves....