Personal observation, probably skewered and colored by anecdotes, but accurate to my memory. I don't have statistics, but it's certainly not a small percentage. To what extent the term voluntary is applicable can be debated as mental health and especially psychological disorders are often in play, but there's no doubt that many refuse opportunities to reestablish themselves in society. I know you work with different social workers, 92, so you may get some insight from them that I lack. I would think that they could affirm the frustration of being unable to help those who choose not to change, though.
You will find that the PC line is "there are no voluntarily homeless people", repeated on practically every website dedicated to homelessness. That is based upon the definition of voluntary, which is where the debate really lies. There's no easy out on this one. It's undeniable that "I choose to be homeless" is not always a forthcoming statement, but I think it's also oversimplification to deny it in totality, and not helpful.
Anyhow, sorry about rambling so much in this thread. This is one of those subjects that I deal with from time to time, though, so it interests me. I will state that while I have had no success in providing long term help to the homeless I have met, I have occasionally enjoyed their company and have been honored to provide a few people I didn't understand a meal or (back when I smoked) a cigarette. I hope I did the right thing.