my mom hung up some clothes of mine on the doorframe and it seriously could not convey more "this guy dresses like a cartoon bully" if it got up and stole a kids lunch money
You watch the "don't go where I can't follow" scene in Return of the King and you ask yourself if Frodo has the doll's eyes reflex.
The doll's eyes reflex can indicate in comatose patients whether the brainstem function is intact - the brainstem is the structure between the brain and the spine where a lot of nerves emerge and intersect.
The doll's eyes reflex is "positive" if you turn the head and the eyes rotate in the opposite direction, thereby continuing to face forward. This means the brainstem is intact, which is good. If you turn the head and the eyes rotate in the same direction, the reflex is "negative," and the brainstem is damaged, which is bad news bears.
Now, in the "don't go where I can't follow" scene, Sam rocks Frodo, and while the motion is not enough to fully test for the reflex, I think (and correct me if I'm wrong), Frodo's eyes do continue to face forward. Therefore, I am just going to pretend the following:
Frodo does have a positive doll's eye reflex, which means he is not dead.
Sam, of course, probably doesn't know this, which is why he assumes that Frodo has perished.