Dropping items while dead - at spawn location
You can drop items while dead. Also, they drop at re-spawn location, not death location.
You are likely teleported to the respawn instantly upon death, but if you cancel the respawn dialog, you can bring up your inventory and drop items while still looking at death location. However, these items will appear at the re-spawn location (tree in surface world).
You can NOT drop items after death in Hardcore Prophecy.