  We point out that the variance of net-baryon distribution normalized by the
Skellam distribution baseline, $\kappa_2[B-\bar{B}]/\langle B+\bar{B}\rangle$,
is sensitive to the possible modification of (anti)baryon yields due to
$B\bar{B}$ annihilation in the hadronic phase. The corresponding measurements
can thus place stringent limits on the magnitude of the $B\bar{B}$ annihilation
and its inverse reaction. We perform Monte Carlo simulations of the hadronic
phase in Pb-Pb collisions at the LHC via the recently developed subensemble
sampler + UrQMD afterburner and show that the effect survives in net-proton
fluctuations, which are directly accessible experimentally. The available
experimental data of the ALICE Collaboration on net-proton fluctuations
disfavors a notable suppression of (anti)baryon yields in $B\bar{B}$
annihilations predicted by the present version of UrQMD if only global baryon
conservation is incorporated. On the other hand, the annihilations improve the
data description when local baryon conservation is imposed. The two effects can
be disentangled by measuring $\kappa_2[B+\bar{B}]/\langle B+\bar{B}\rangle$,
which at the LHC is notably suppressed by annihilations but virtually
unaffected by baryon number conservation.
