Stars and planets orbit a common point, called a barycenter. Planets don’t technically orbit the stars, they both swing around the barycenter. Think of two people holding hands and twirling around.
The only difference is that one person is King Kong, the other is a child. King Kong will *always* be in the middle, the child will never be able to swing King Kong around them.
So no, a planet will never orbit a star. A tiny red-dwarf and a large brown-dwarf might orbit a barycenter that’s outside the surface of either though.
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