try using a multi meter, set to continuity test, clip one end of the multi meter lead and the other, touch around the geetar part, anywhere as long as theres metal parts. If the wire is connected to anything metal, you should hear a beep sound from the multi meter.
another way, find a long thin jumper wire, poke it into the hole and see where it leads to. If the wire can come out from nowhere, there should be another hole at the other end where the wire originated from. Heh, it wont be logical if the wire just come out from the wood and at the other end, not connected to anywhere
if that wire can be removed, most likely its linked to the bridge and it came off when you remove the bridge. All metallic part on the electric geetar need to be grounded, the bridge is no exception. Sometime it doesnt have to be soldered to the bridge. As long as the wire sit under the bridge and come into contact with the any metallic/counductable area, the bridge will be grounded.
Another reason why i believe that the wire is the ground wire for bridge coz its connected to the back of the pot in the pic and for the various geetar i have seen, almost all came out from nowhere and connect to ground(can be at the back of the pot or straight to the negative/ground/sleeve point on the output jack)