So I was going to name this "Looking for an even that fires when you close a chest" but then I realized for my purposes I'd need that for every that has an inventory you can access.
So armor stands, Item frames, those weapon holders from custom NPCS that are really cool.
With that realization the question has become bigger and my first two knee jerk reactions to deal with it are:
Can I some how extend or access the Blocks Class file to tap into event that fire when players take things from the inventory? Which I guess is a java question but it's something I wish I could do all the time so I'll ask any where.
Or option B:
Is their some way I can solve this by utilizing whatever system mine craft uses to save all the inventories any way?