  Motivated by the newly observed $^{39}$Na in experiments, systematic
calculations of global nuclear binding energies with seven Skyrme forces are
performed. We demonstrate the strong correlation between the two-neutron
separation energies ($S_{2n}$) of $^{39}$Na and the total number of bound
nuclei of the whole nuclear landscape. Furthermore, with calculated nuclear
masses, we perform astrophysical rapid-neutron capture process ($r$-process)
simulations by using nuclear reaction code TALYS and nuclear reaction network
code SkyNet. $r$-process abundances from ejecta of neutron star mergers and
core-collapse supernova are compared. Prominent covariance correlations between
nuclear landscape boundaries and neutron-rich $r$-process abundances before the
third peak are shown. This study highlights the needs for further experimental
studies of drip-line nuclei around $^{39}$Na for better constraints on nuclear
landscape boundaries and $r$-process.
