Anomalous plasma can arise in dense plasmas as a consequence of the development resistivity of the Lower Hybrid drift Instability (LHI), which is triggered whenever the electron drift velocity becomes comparable to or larger than the thermal ion velocity. This effect was carefully evaluated for theta-pinch plasmas and later on used in the modelling of denser pinches, like Plasma Focus columns or Z-pinches, because of the diverging electron drift velocity expected in the classical equilibrium (uniform current, parabolic plasma density) pinch. Conceptually, the possibility of diverging drift velocities is far more a general situation than Z-pinches, and in this work we study it, in general, for plasma-magnetic field interfaces existing in other configurations, like that found in devices producing travelling current sheets (Plasma Focus devices, imploding pinches, etc.). We show that it is essential to account for this effect in steady state situations, and that it could be also important in the time varying ones.