How to create a circular armature? let's say I wanted to rig and animate a torus. — is it possible to have a circular armature?

from what I can tell, this is not possible. so I thought maybe it's an idea to add a driver to the tail position of the last bone, that gets the head position of the first bone. however, this also doesn't seem to be an option.
The thing, what you want to build will cast loop in parents (circular dependency), it doesn't allow. When Blender calculates bones coordinates, it moves from child through parents to root bone. And if you have loop in parents, blender can't find root bone

To avoid circular dependency you can bild rig like this:





This type of rig you can find in BlenRig, in lips rigging