It has recently been demonstrated via nonequilibrium molecular dynamics (NEMD) simulation [M. H. Nafar Sefiddashti, B. J. Edwards, and B. Khomami, J. Chem. Phys. 148, 141103 (2018); Phys. Rev. Lett. 121, 247802 (2018)] that the extensional flow of entangled polymer melts can engender, within a definite strain-rate regime [expressed in terms of the Deborah number (De) based on the Rouse time], the coexistence of separate domains consisting primarily of either coiled or stretched chain-like macromolecules. This flow-induced phase separation results in bimodal configurational distributions, where transitions of individual molecules between the coiled and stretched states occur very slowly by hopping over an apparent energy activation barrier. We demonstrate that the qualitative aspects of this phenomenon can be described via the single-mode Rolie-Poly model including Convective Constraint Release (CCR) and finite extensibility of the chain-like macromolecules. This analysis reveals the physical mechanism for the configurational coexistence, namely, the nonlinear rate of change of the average entropic restoring force of a given entangled chain with extension. Under conditions of significant flow-induced disentanglement, the rate of change of the effective restoring force initially decreases with extension (effective spring softening) and then increases (hardens) as the maximum chain length is approached. When balanced by flow-induced chain stretching, we find that there can be two configuration states within the same De regime, as covered by the NEMD simulations; therefore, a region of conformational coexistence can indeed exist. However, we demonstrate that this coexistence of configurational microstates is only possible when the magnitude of the CCR parameters is consistent with the rate of flow-induced disentanglement, as observed in the NEMD simulations.