In protoplanetary discs, the inner radial boundary between the MRI turbulent (‘active') and MRI quiescent (‘dead') zones plays an important role in models of the disc evolution and in some planet formation scenarios. In reality, this boundary is not well-defined: thermal heating from the star in a passive disc yields a transition radius close to the star (<0.1 au), whereas if the disc is already MRI active, it can self-consistently maintain the requisite temperatures out to a transition radius of roughly 1 au. Moreover, the interface may not be static; it may be highly fluctuating or else unstable. In this paper, we study a reduced model of the dynamics of the active/dead zone interface that mimics several important aspects of a real disc system. We find that MRI-transition fronts propagate inwards (a ‘dead front' suppressing the MRI) if they are initially at the larger transition radius, or propagate outwards (an ‘active front' igniting the MRI) if starting from the smaller transition radius. In both cases, the front stalls at a well-defined intermediate radius, where it remains in a quasi-static equilibrium. We propose that it is this new, intermediate stalling radius that functions as the true boundary between the active and dead zones in protoplanetary discs. These dynamics are likely implicated in observations of variable accretion, such as FU Ori outbursts, as well as in those planet formation theories that require the accumulation of solid material at the dead/active interface.