  Using $N$-body+SPH simulations of galaxies falling into a cluster, we study
the evolution of their radial density profiles. When evolved in isolation,
galaxies develop a type~II (down-bending) profile. In the cluster, the
evolution of the profile depends on the minimum cluster-centric radius the
galaxy reaches, which controls the degree of ram pressure stripping. If the
galaxy falls to $\sim 50\%$ of the virial radius, then the profile remains
type~II, but if the galaxy reaches down to $\sim 20\%$ of the virial radius the
break weakens and the profile becomes more type~I like. The velocity
dispersions are only slightly increased in the cluster simulations compared
with the isolated galaxy; random motion therefore cannot be responsible for
redistributing material sufficiently to cause the change in the profile type.
Instead we find that the joint action of radial migration driven by
tidally-induced spirals and the outside-in quenching of star formation due to
ram pressure stripping alters the density profile. As a result, this model
predicts a flattening of the age profiles amongst cluster lenticulars with
type~I profiles, which can be observationally tested. %
