I'm trying to change the properties of an object after it has been dropped from the inventory. Since the object no longer seems to be an "object reference," I can't work out a way to make it a property for my script. Any thoughts?

There's a story manager event that fires when an object is dropped. You could use that to launch a quest, and thus run a script.

Are you using http://www.creationkit.com/OnItemRemoved_-_ObjectReference?

I think you'd need to check for the akBaseItem instead of the akObjectReference.

Or what DocClox said. It sounds like a sound plan.

Thank you, for you responses, akBaseitem was what I was looking for. Teaching myself Papyrus with the tutorials, and grasping concepts slowly

Checking akObjectReference is safe as long you as you make your object persistent. Assuming you know the object before dropping it you can make it persistent. Eg: if you have it in a quest alias it won't be enough to have it persistent i believe, but if you have it you can put an registedForUpdate on it anytime then unregisterForUpdate from onItemRemoved where you also do your stuff.
Bottom line if akObjectReference is not None, and won't be if persistent, you can safely use it.