  We show that the yield ratio of free spectator neutrons produced in
high-energy $^{96}$Zr+$^{96}$Zr to $^{96}$Ru+$^{96}$Ru collisions is a clean
probe of the neutron-skin thickness of colliding nuclei and the slope parameter
$L$ of the symmetry energy. The idea is demonstrated based on the proton and
neutron density distributions via a state-of-the-art
Skyrme-Hartree-Fock-Bogolyubov calculation. Among spectator nucleons given by
the Glauber model, free spectator neutrons include those from direct production
that survive from clusterization as well as those from deexcitation of heavy
clusters described by the popular GEMINI model. More free neutrons are produced
in collisions of $^{96}$Zr nucleus due to its larger neutron skin, compared to
those produced in collisions of $^{96}$Ru nucleus with a smaller neutron skin.
The difference of the free spectator neutron yield is further increased with
the increasing difference of the neutron-skin thickness between $^{96}$Zr and
$^{96}$Ru with a larger $L$ value, and the increase in ultracentral collisions
is particularly insensitive to model details and experimental uncertainties.
Since the production of free spectator neutrons is not affected by the
complicated dynamics in the mid-rapidity region, the ratio of their
multiplicities in ultracentral isobaric collisions is a robust observable for
constraining the neutron skin and $L$ value.
