  The existence of a classical bulge in disk galaxies holds important clue to
the assembly history of galaxies. Finding observational evidence of very low
mass classical bulges particularly in barred galaxies including our Milky Way,
is a challenging task as the bar driven secular evolution might bring
significant dynamical change to these bulges alongside the stellar disk.
  Using high-resolution N-body simulation, we show that if a cool stellar disk
is assembled around a non-rotating low-mass classical bulge, the disk rapidly
grows a strong bar within a few rotation time scales. Later, the bar driven
secular process transform the initial classical bulge into a flattened rotating
stellar system whose central part also have grown a bar-like component rotating
in sync with the disk bar. During this time, a boxy/peanut (hereafter, B/P)
bulge is formed via the buckling instability of the disk bar and the vertical
extent of this B/P bulge being slightly higher than that of the classical
bulge, it encompasses the whole classical bulge. The resulting composite bulge
appears to be both photometrically and kinematically identical to a B/P bulge
without any obvious signature of the classical component. Our analysis suggest
that many barred galaxies in the local universe might be hiding such low-mass
classical bulges. We suggest that stellar population and chemodynamical
analysis might be required in establishing the evidence for such low-mass
classical bulges.
