I've hospiced plenty of folks right until they've passed and that feeling of missing comes sooner than clinical death, I'll tell you. Once someone's respiration rate drops low enough and their pulse and BP are undetectable, and the blood starts pooling, you'll have a very hard time differentiating them from a body without a stethoscope and time. Clinically dead folks do tend to become a job to deal with and aren't something that register as people, though you still feel the need to be respectful.