Hello,
Your son's comments about death need to be acknowledged by his treatment center IMO. I find it very surprising that no one there is addressing his desire to die or communicating with you about how they're approaching it/him. Have you tried calling the facility?
I see in your post that he has little trust in the people he's with and that might explain why he continues to reach out to your family and relay the same message. His comments need to be addressed by a professional.