Is it possible for the remnants of a planet to be locked in orbit around another in a dual planet system?

I'm envisioning a double-planet system where both orbit around a central point. One planet is approximately Earth-sized, while the other is about one-tenth the size.

One of the planets (the smaller one) in this system has seen a catastrophe that has left about half or three-quarters of it as a cohesive whole while the rest is just rocks and space dust.

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Is it possible for the remnants of a planet to be locked in orbit around another in a dual planet system?

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