BT will install a new cabinet close to (could be 50metres) the existing cabinet and then run a tie cable between the two. The fibre (normally several) is run through the BT ducts to that new cabinet.
When you have FTTC installed the technician goes to the existing cabinet and disconnects your"pair from the frame. He then connects a pair in the tie cable to the frame and connects your pair to the return part of the tie cable.
So, your line goes from exchange to cabinet, then through the tie cable to the new cabinet and DSLAM where the VDSL signal is added to the voice line. This combined signal is fed back across the tie pair to the original cabinet where it joins the copper pair to your house.
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