We have defined pinning fields as those random fields that keep some of the magnetic moments unreversed in the region of negative external applied field during the demagnetizing process. An analysis of the statistical properties of such pinning fields is presented within the context of the Gaussian Random Field Ising Model (RFIM). We show that the average of the pinning fields exhibits a drastic increase close to the coercive field and that such an increase is discontinuous for low degrees of disorder. This behaviour can be described with standard finite size scaling (FSS) assumptions. Furthermore, we also show that the pinning fields corresponding to states close to coercivity exhibit strong statistical correlations. ; Comment: 9 pages + 6 figures