Answer: A palm tree can be propagated by root division (separating out sucker shoots), so if your neighbor's plant has any latent suckers, it may regenerate from its rootball. I'd keep the rootball moist and see what happens.
However, unlike other types of plants, you can't root a palm tree cutting, so I'm afraid the broken-off top is destined for the compost pile. And palm tree seeds are borne in fruits, so I don't think what you're seeing on the stalks are seeds, but rather other reproductive structures.
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