  The importance of microphysical inputs from laboratory nuclear experiments
and theoretical nuclear structure calculations in the understanding of the core
collapse dynamics, and the subsequent supernova explosion, is largely
recognized in the recent literature. In this work, we analyze the impact of the
masses of very neutron rich nuclei on the matter composition during collapse,
and the corresponding electron capture rate. To this aim, we introduce an
empirical modification of the popular Duflo-Zuker mass model to account for
possible shell quenching far from stability, and study the effect of the
quenching on the average electron capture rate. We show that the preeminence of
the $N=50$ and $N=82$ closed shells in the collapse dynamics is considerably
decreased if the shell gaps are reduced in the region of $^{78}$Ni and beyond.
As a consequence, local modifications of the overall electron capture rate up
to 30\% can be expected, with integrated values strongly dependent on the
stiffness of magicity quenching and progenitor mass and potential important
consequences on the entropy generation, the neutrino emissivity, and the mass
of the core at bounce. Our work underlines the importance of new experimental
measurements in this region of the nuclear chart, the most crucial information
being the nuclear mass and the Gamow-Teller strength. Reliable microscopic
calculations of the associated elementary rate, in a wide range of temperatures
and electron densities, optimized on these new empirical information, will be
additionally needed to get quantitative predictions of the collapse dynamics.
