Casting Demonic Embrace with the permission granted by its last ability doesn't change when you can cast it.

If another effect gives you permission to cast Demonic Embrace from your graveyard, you don't pay the additional cost imposed by its last ability if you use that permission.

If the enchanted creature dies during your turn, you receive priority before any other player does. If you're allowed to cast Demonic Embrace at that time, you may do so before any player can attempt to remove it from your graveyard.