A new electromagnetic quasi-neutral time-dependent implicit hybrid model for simulating the slow-mode switch-off shock is developed, in which the electrons are treated as a finite-mass adiabatic fluid (gamma sub e = 5/3), whose motion along the shock normal provides local charge neutrality. The model is used to examine the effects of various boundary conditions applied during shock formation. It is shown that, for each upstream condition, two distinctly different slow-shock structures can be obtained: a low-shock structure with a trailing magnetic wave (TMW) and a slow-shock structure without a TMW, depending strongly on the boundary conditions for the electric and magnetic fields at the physical piston which generates the shock. The results indicate that the slow-shock structure with a TMW is nonlinearly unstable with respect to changes in the upstream magnetic field, suggesting that the downstream structure of slow shocks need not be associated with a TMW.