The tube model, which reduces the interaction of many-chain entanglement to a single-chain picture, has enabled quantitative descriptions of the mechanical behaviors of polymeric materials and underpins applications from polymer processing to life sciences. In strong extensional flows, however, this theory systematically fails. Herein, through molecular dynamics simulations of entangled polymers, we reveal a strain-induced crossover from the entangled state to a packed state in the inter-chain configuration. Following the saturation of primitive chain stretch, convective disentanglement and chain alignment reorganize the system into a packed configuration of aligned segments. This crossover fundamentally alters the origin of the stress in nonlinear extensional flows, which explains the breakdown of the tube model under such conditions, and leads to a quantitative prediction to the mechanical response at large extensional strains. These findings clearly show how the collective inter-chain reorganization governs the nonlinear extensional behaviors.