Fake Recycle Bin via Group Policy

There's no stock functionality in the product to do what you're looking for. I'm sure somebody could come up with a crazy hack that would give you 85% of what you wanted, but that last 15% to make it work would likely have to involve rather invasive modifications to Windows (or, at least, third-party software). Group Policy will let you run arbitrary code on startup or logon, so making something do what you want that's invoked by Group Policy is certainly possible, but what you want isn't any kind of stock functionality.

You're going about this the wrong way. The files you're looking to "recover" from a "dirty resignation" should already be stored in locations that are covered by your regular backup. Recover of these files should be a matter of restoring a backup. If you're storing important data (files that might need to be "recovered") in a location that's not covered by backup then you've got a lot bigger problems than a "dirty resignation".