  We study the trend of the nuclear symmetry energy in relativistic mean-field
models with appearance of the hyperon and quark degrees of freedom at high
densities. On the pure hadron level, we focus on the role of $\Lambda$ hyperons
in influencing the symmetry energy both at given fractions and at charge and
chemical equilibriums. The softening of the nuclear symmetry energy is observed
with the inclusion of the $\Lambda$ hyperons that suppresses the nucleon
fraction. In the phase with the admixture of quarks and hadrons, the equation
of state is established on the Gibbs conditions. With the increase of the quark
volume fraction in denser and denser matter, the apparent nuclear symmetry
energy decreases till to disappear. This softening would have associations with
the observations which need detailed discriminations in dense matter with the
admixture of new degrees of freedom created by heavy-ion collisions.
