The stories say Chen Tuan slept for months at a time on Mount Hua and had to be checked to see whether he had died. Read as biography that is anecdote. Read as a description of a practice it points at something the Daoist tradition took seriously.
Inner alchemy works by reversing the ordinary outward flow of vitality, and the states it aims at are described in terms of stillness, minimal breathing and a return to an embryonic condition. A body of technique associated with Chen Tuan's name treats sleep as the vehicle for this: lying postures with the limbs arranged in particular ways, breath allowed to become almost imperceptible, and the mind kept from dispersing rather than kept awake. Later collections of sleep exercises circulate under his name, and whatever their actual authorship they show what the tradition understood him to have taught. The distinction the sources insist on is between dozing and this, which is closer to sitting in oblivion lying down.
His refusals of office belong to the same picture. Repeatedly summoned by emperors, he came, spoke, and went back to the mountain, and the last Song emperor to call him granted him an honorific title instead of a post. That pattern was already old in China and he made it definitive: the hermit who cannot be recruited increases in authority precisely by declining, and a dynasty gains legitimacy by being seen to seek him. Later paintings and stories fix him in that role, asleep on a rock or riding a donkey backwards, indifferent to a court that wants him.