I’ll take “Star orbit a planet” to mean that the Lagrange point is closer to the star than the planet (meaning the planet is much, much more massive, and the star tends to go around the planet rather than the other way around)
Given how stars and star systems form, it’s *very* unlikely. Dust clouds swirl around what eventually becomes a star. The star is where most of the mass – over 99% – from the star system is concentrated. There just isn’t enough left in the local dust clouds for a planet that big.
But still, in the scheme of the universe, strange things can still happen. A burned out star can look a lot like a planet, and every once in a while two solar systems can go careening through each other, enough to mix things up, and a dead star bigger than the star at the middle of a tiny star system could pull that star into its orbit.
So it’s a maybe.
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