The National Catholic Bioethics Center has a website and on it an article detailing the Church's teaching on end-of life issues. They are in line with the Magisterium of the Church.
As far as who would have to pay for the health care, I'm not sure. Sometimes hospitals write off expenses. I do know you can purchase long-term health care insurance, although I'm not sure if it applies to medical treatment or just nursing home care. That's certainly something to check into.