I am assuming you are talking of the rectangular surround. If the centre piece is there with the four pins you can recover your data from the usb drive.
With the PC turned off remove the broken piece from the USB socket.
Can you re-attach this easily?, can you open the stick and ensure the surround is connected to ground?
Either way the stick drive should work as long as it has the four main pins in good contact with the connections in a socket, so make sure you insert correctly and use plain paper or something as a wedge to hold it in place. (if i remember correctly the two outer most pins are +5v and ground and the drive wont work at all if these dont have good contact)
Recover you data and bin the faulty stick.
Daniel
November 2008