Current flowing in the BPE because it provides less resistive current path than the electrolyte. As illustrated in the Figure; as consequence of the current entering side (D/Blue) from the anode, side D will polarise cathodically (potential will become more negative). At the other hand, side (B/Red) where the current is leaving, it will polarise anodically (potential will become more positive) and will corrode. This is due to polarisation which occurs opposite to the current direction. 
This theory is almost accepted in all classic  and recent cathodic protection books, and NACE publications and standards, as explanation of corrosion and coating disbondment caused by DC interference between pipelines and different structures (e.g. cathodically protected or unprotected structures, railways and HVDC). This because it is more suitable for large-scale structures in highly resistive, heterogeneous environments where solution potential (V) plays a less pivotal role and the reactions are primarily concentrated only at the poles (where current enters and leaves).