We establish a correspondence between systems with strongly repulsive and strongly attractive contact interactions for a number of one-dimensional, many-body models. Our findings extend thetheoretical results connected with super-Tonks-Girardeau gas to highly non-equilibrium dynamics in the presence of strong attraction. We specify a class of initial states for which attractive forceseffectively act as strongly repulsive cores during the dynamics. The novel mechanism is illustratedon the prototypical problem of the domain stability in two-component Fermi gas. Additionally,we provide a discussion of non-local interactions and analyze possible universality of the presented results.