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In heavy nuclei the ratio between local densities of neutrons and protonsincreases towards the nuclear periphery. The excess of neutrons is known as theneutron skin (NS) with a subtle difference ($<0.5$~fm) between the r.m.s radiiof the distributions of neutrons and protons. We show that the presence of NSin $^{208}$Pb leads to extra spectator neutrons in ultracentral$^{208}$Pb--$^{208}$Pb collisions at the CERN SPS and LHC. The yields ofspectator neutrons and protons were calculated within a new version ofAbrasion-Ablation Monte Carlo for Colliders model (AAMCC-MST) taking intoaccount NS and pre-equilibrium clustering of spectator matter. While theaverage numbers of spectator neutrons and protons in ultracentral collisionsvary insignificantly, the cross sections of emission of certain numbers ofspectator neutrons in events with 0,1,...5 spectator protons are changed by50--250\%, depending on the thickness of NS. These cross sections are lesssensitive to other parameters in calculations, and their measurements in theALICE experiment at the LHC will make it possible to restrict the existingvariety of neutron density parameterizations in $^{208}$Pb.

Peeling away neutron skin in ultracentral collisions of relativistic nuclei