Board Thread:Off Topic/@comment-199.168.131.155-20191001134003/@comment-26213507-20191001170741

The second you die in Skyrim enemies ignore you, so no, they won't interact with the Dragonborn's body in any way, including taking the Jagged Crown.

In terms of lore, everyone wants the Jagged Crown so maybe, although this never plays into the game besides when first getting to Korvanjund.