We analyze the dynamics of one-dimensional quantum gases with strongly attractive contact interactions. We specify a class of initial states for which attractive forces effectively act as strongly repulsive ones during the time evolution. Our findings extend the theoretical results on the super-Tonks-Girardeau gas to a highly nonequilibrium dynamics. The mechanism is illustrated on the prototypical problem of the domain stability in a two-component Fermi gas. We also discuss finite-range interactions and analyze the universality of the presented results. Moreover, we use our conclusions to argue for the existence of metastable quantum droplets in the regime of strongly attractive contact and attractive dipolar interactions.