The chain stabilizer (blue in the sketch below; source) consists of two parts.
The two parts are:
- an outer metal part (top right of the image below), and
- an inner part (bottom left of the image below).
In this video Truman shows the inner part and stresses that its outer cyclindrical surface should be lubricated (by a high-performance grease, because under use the friction can generate heat as high as 450F), but that the flat top should not be lubricated—as the instructions on Shimano's site also say.
It is evident from the video that the inner part is itself made from two materials.
Despite sharing the same name, this is quite distinct from the clutch in cars with manual transmission. How does it work? (Why does it rotate with less—or no—friction clockwise, but resists movement when rotated counterclockwise?)
Ideally you've used up one such part and were too curious not to break it apart and look inside, in which case it would be perfect if you can share with us what you saw.
The present question is a sequel to this question. That question asks how an RD clutch works from the outside (how it is used). The present question asks how it works on the inside.
The earliest this tech was described is April 25, 2011 (that I've found).