I don't have a citation handy. I had a college class on homelessness some years ago. I have read a fair amount about poverty. I am currently homeless. My medical handicap is a primary underlying cause of my lack of housing and challenges involved in trying to resolve that.
It is too late to edit the comment. It may not be "most" poor people (ie more than 50%) but it is certainly many.
I can also confidently state that a high percentage of homeless individuals have either a medical or a mental health condition that is an underlying cause of homelessness hy substantially interfering with their ability to make their life work. I believe that for the homeless population this is well over 50%, though I don't have a citation for that either. However, my previous college class and firsthand experiences suggest that health problems lead to homelessness. I know that once you are on the street, it can be hard to take care of yourself and homelessness often does cause or worsen health issues. I think this reality masks the degree to which health problems both precede and contribute to incidence of homelessness. I think most people think people on the street are ill because they are on the street. But everything I have seen indicates most of them were ill before they became homeless and that fact contributed to them ending up on the street or outright caused their homelessness. In many cases, being on the street does cause a worsening of their health, but that should not be misconstrued as "Well, they are only ill because they are homeless."
Everyone I have ever known reasonably well who had a serious health crisis experienced significant financial stress as a consequence, above and beyond the high medical expenses per se. Some things I have heard over the years: Job loss, time away from the job, passed over for promotion, took a demotion to a lower paying position. There are also additional expenses incurred beyond the medical expenses, such as higher food costs due to being too sick to work, transportation expenses if they need to travel to get care, etc.
I also recall reading in an article that the most common factor in cases where women were on welfare for very long periods and could not seem to get off welfare was that she was de facto responsible for providing care for a relative with high needs of some sort, either a special needs child or elderly parent in poor health or similar scenario.