The consequences of the sudden change in the coupling constants (quenches) on the phase structure of the theory at late times are explored. We study in detail the three-dimensional φ6 model in the large-N limit and show that the φ6 coupling enjoys a widened range of stability compared to the static scenario. Moreover, a new massive phase emerges, which for sufficiently large coupling becomes the dominant vacuum. We argue that these novel phenomena cannot be described by a simple thermalization effect or the emergence of a single effective temperature.