  Background: Deep-inelastic scattering (DIS) on the deuteron with spectator
nucleon tagging represents a unique method for extracting the free neutron
structure functions and exploring the nuclear modifications of bound protons
and neutrons. The detection of the spectator (with typical momenta $\lesssim$
100 MeV/c in the deuteron rest frame) controls the nuclear configuration during
the DIS process and enables a differential analysis of nuclear effects. At the
future electron-ion collider (EIC) such measurements will be performed using
far-forward detectors.
  Purpose: Simulate deuteron DIS with proton or neutron tagging with the
baseline EIC far-forward detector design. Quantify detector acceptance and
resolution effects. Study feasibility of free nucleon structure extraction
using pole extrapolation in the spectator momentum.
  Methods: DIS events with proton and neutron spectators are generated using
the BeAGLE Monte Carlo generator. The spectator nucleon momentum is
reconstructed including effects of detector acceptance and resolution. Pole
extrapolation is performed under realistic conditions. The free nucleon
structure extraction is validated by comparing with the input model.
  Results: Proton and neutron spectator detection is possible over the full
transverse momentum range $0 < p_T < 100$ MeV/c needed for pole extrapolation.
Resolution effects on the distributions before corrections are ~10% for proton
and ~30 for neutron spectators. The overall accuracy of nucleon structure
extraction is expected to be at the few-percent level.
  Conclusions: Free neutron structure extraction through proton tagging and
pole extrapolation is feasible with the baseline EIC far-forward detector
design. The corresponding extraction of free proton structure through neutron
tagging provides a reference point for future studies of nuclear modifications.
