Bezier circle shrinkwrapped on sphere. Empty doesn't follow path. I accidentally captured this with the curve origin moved to the empty, but that doesn't affect the issue.
@lemon provided a renderable visualization. Here the curve I'm later referring to is visualized as a slim torus, which keeps its' thiccness diameter and turns into a sphere, of the said diameter, when it's at the poles.
I keep saying animation, but I don't mean rendered animation, when there's no surface or thickness.
Basically replace the torus in lemons animation with a curve... Edit: shrinkwrap makes the curve move along the sphere, but objects don't follow the path, so my guess is that objects projected from it/ based upon it also wouldn't.
Any method, Python, Animation Nodes preferable.