Heh, that's kind of amusing. I hope you don't mind my chuckling!
The piece that came out looks like a piezo transducer/sounder/buzzer/etc. I'm accustomed to seeing just two wires on them but yours has three. It probably isn't damaged, so if you want to repair the box it's likely possible with just a little bit of soldering. The wires look like they probably broke at the point where the insulation was stripped. If you open the housing and look carefully at the shape of the ends of the wires, their lengths, the way the strands broke, etc you may be able to make a good guess as to how they should match up. You'd have to figure out how to activate the buzzer in order to test the success of the repair though. The good news is that if the wires weren't matched correctly there'd probably be no permanent damage.