In the late stage of a substorm growth phase, the magnetic field in the near-Earth region is highly stretched. We assume that such conditions can lead to violation of the frozen-in-flux condition, allowing transfer of plasma from one flux tube to another and creating a plasma blob tailward of a plasma bubble. In this letter we present results of a simulation where we artificially impose a bubble-blob pair by introducing a disturbance in PV5/3 in the near-Earth plasma sheet. In the subsequent evolution, as calculated by the equilibrium version of the Rice Convection Model (RCM-E), the bubble surges earthward and the blob moves tailward, while the magnetic field between them weakens and the localized cross-tail current density increases. We speculate that, at substorm onset, there could be a positive feedback in which the breakdown of the frozen-in condition would increasingly make the current sheet thinner until magnetic reconnection occurs.