Is the plug flush to the case?
If it is you might be able to snag it with a small drill bit and a small screwdriver to hold the core steady.
What you need to do here is make sure the core does not move as you hand drill the drill bit into the center of the plug. Once you get a good bite pull it straight out. Remember the idea is to grab not drill so you want to go slow and remember the bite won't be very strong so you have to take care not to pull to quickly or at an angle. A dental probe might also work here.
What ever you do don't try any glue as it's more likely make things worse!
If the core is below the edge you'll need to take the unit apart to poke it out from the inside.