As an extension of recent work on two-dimensional light-front ϕ4 theory, we implement Fock-sector dependence for the bare mass. Such dependence should have important consequences for the convergence of nonperturbative calculations with respect to the level of Fock-space truncation. The truncation forces the self-energy corrections to be sector dependent; in particular, the highest sector has no self-energy correction. Thus, the bare mass can be considered sector dependent as well. We find that, although higher Fock sectors have a larger probability, the mass of the lightest state and the value of the critical coupling are not significantly affected. This implies that coherent states or the light-front coupled-cluster method may be required to properly represent critical behavior.