Mysterious current flow through socket
The socket is being used as a switch. Usually these contain a switch contact to allow disconnection of the battery power when the plug is inserted and reconnection when the power jack is removed. Figure 1 shows a typical example.



Figure 1. A guitar stomp-box with battery and external power input. Note that this arrangement is using a switched positive. Yours may be using a switched negative. Source: DIY Strat.

If you have no contact between A and C when the jack is removed then it is likely that the socket is broken.