  We explore the impact of neutron-rich nuclei masses on the symmetry energy
properties using the mass table evaluated by the deformed relativistic
Hartree-Bogoliubov theory in continuum (DRHBc) model. First, using the
semi-empirical mass formula with the DRHBc mass table, we investigate the
symmetry energy at saturation density $\rho_0$, denoted as $S_0$, and the ratio
of surface to volume contributions to the symmetry energy, $\kappa$. As a
result, we obtain $S_0=27.85\,{\rm MeV}$ ($\kappa=1.38$) for $a_{\rm sym}(A)
=S_0 (1 - \kappa A^{-1/3})$ (Type I) and $S_0=32.66\,{\rm MeV}$ ($\kappa=3.15$)
for $a_{\rm sym}(A) = S_0 (1 + \kappa A^{-1/3} )^{-1}$ (Type II), which are
lower than those obtained using the AME2020 mass table, $S_0=28.54\,{\rm MeV}$
($\kappa=1.29$) for Type I and $S_0=33.81\,{\rm MeV}$ ($\kappa=3.04$) for Type
II. Second, we further investigate the effect of these changes in $a_{\rm
sym}(A)$ on the density-dependent symmetry energy by employing the empirical
model of $S(\rho) = C_k(\rho/\rho_0)^{2/3} + C_1(\rho/\rho_0) +
C_2(\rho/\rho_0)^{\gamma}$ and universal relation of $a_{\rm sym}(A=208) =
S(\rho=0.1\,{\rm fm}^{-3})$. Compared to the experimental constraints, we find
that $S_0$ and slope parameter $L$, determined by the DRHBc mass table with
Type II, are more suitable to explain the constraints by heavy ion collisions
and isobaric analog states than AME2020. We also discuss the neutron skin
thickness derived from the $L$, comparing it with experimental measurements.
