What module lets you delete a node after a specific time if its unpublished?
You could do this using the Rules module.  If you enable the built-in scheduler submodule, you could create a set of rules/components like this (rough code to give you an idea, not a step-by-step walkthrough):

Component to delete content (Action set)


Action: Delete content


Rule to schedule content deletion (Rule)


Event: Content is created
Action: Schedule the "Component to delete content" after the specified amount of time


Rule to clear deletion on publishing (Rule)


Event: Content is published
Action: Delete the scheduled event for that piece of content ("Component to delete content")