At forward rapidities and high energies we expect to probe non-linear effects of the Quantum Chromodynamics (QCD). One of the most promising observables to constrain the QCD dynamics at this regime is the exclusive vector meson photoproduction (EVMP). We study the EVMP in association with a leading baryon (product of the proton dissociation) in photon-hadron interactions that take place in $pp$ and $p$Pb collisions at large impact parameters. We present the rapidity distributions for $\rho$ and $J/\psi$ photoproduction in association with a leading baryon (neutron and delta states) at LHC run 2 energies. Our results show that the $V + \Delta$ cross section is almost 30 % of the $V + n$ one. Our results also show that a future experimental analysis of these processes is, in principle, feasible and can be useful to study the leading particle production.