When parsing the noun phrase...which is modifying which?
It would be unfair to search any meaning -literal or metaphorical- in the given sentence. If we reduce the sentence to the bare minimum what remains is, FEELING IS PAIN. We know not how it feels to DIE when death is total extinction. The sentence at best attempts to suggest, "The feeling closest to death is pain".
The subject proper is " FEELING ". 'Closest to death' is an an adjective phrase, elliptical form of the clause, 'which is closest to death' qualifying 'feeling' an abstract noun.
Structurally be what may, the noun phrase taken altogether- the feeling closest to death- the focus of emphasis shifts to " DEATH" even though the nucleus subject is feeling as before. And the sentence goes to mean-- excruciating pain is akin to death. However the paradox remains we cannot know death!