The story is definitely pre-00's, possibly quite older.
The general gist is: The protagonist goes into a hibernation state after some procedure he undergoes or accident that happens to him.
His wife(?) or a friend calls for doctor(s?). They try to wake him up, but to no avail. As his heart rate drops to something like two beats per minute or one beat every four minutes, they almost make a mistake of considering him dead.
In the following days the protagonist, while hibernating, gets covered with an almost impenetrable green-ish cocoon, and his doctor has trouble getting blood sample from him, breaking a few needles. He manages to extract a sample with a medical drill. The blood is pale-pink in color and does not resemble the human blood, possessing extreme amounts of anti-bacterial agents.
At some point, I think, the doctor expresses an opinion that the protagonist is undergoing an insect-like cocoon phase and his whole body is dissolved inside the shell. However, I could be mistaken.
After a while the cocoon cracks and the protagonist emerges from it without any noticeable change. Being unable to find anything wrong with the apparently cured patient, the doctor departs, quite puzzled.
Being left alone, protagonist lights a cigarette, walks out into a field or a meadow, then takes off the ground and levitates himself to space.
I have read this in the 90's, however, it can be much older than this. I have a feeling the piece is named "Imago" (could be wrong), but I have had no success finding anything about it online, and I don't know who's the author.