  We revisit the calculation of the fermion self-energy in QED in the presence
of a magnetic field. We show that, after carrying out the renormalization
procedure and identifying the most general tensor structure for the modified
fermion propagator, when working in the large field limit, the mass function
develops an imaginary part. This happens when account is made of the
sub-leading contributions associated to Landau levels other than the lowest
one. The imaginary part is associated to a spectral density describing the
spread of the mass function in momentum. The center of the distribution
corresponds to the magnetic-field modified mass. The width becomes small as the
field intensity increases in such a way that for asymptotically large values of
the field, when the separation between Landau levels becomes also large, the
mass function describes a stable particle occupying only the lowest Landay
level. For large but finite values of the magnetic field, the spectral density
represents a finite probability for the fermion to occupy Landau levels other
than the LLL.
