I found this and have no idea what it is. I want to put in in the lost and found, but under what category? I thought it might be some kind of belt clip for a GPS device.

Can't tell much from the second photo but it looks like one of those belt clip-ons with the retractable cord that people use with passcards.

Kind of like this:
http://www.identificationsolutions.co.uk/images/products/badge-reel--yoyo-reels/Security%20ID%20Card%20Badge%20Reel%20with%20Belt% 20Clip%202120-3002%20a.png

Thank you! I think you are right. It appears to be a broken one. :o I'm a goof.