While cold dark matter numerical simulations predict steep, `cuspy' density profiles for dark matter halos, observations favor shallower `cores'. The introduction of baryonic physics alleviates this discrepancy, notably as feedback-driven episodes of impulsive gas outflow and inflow can expand the dark matter distribution. Such episodes can also affect the stellar component and explain the formation of Ultra Diffuse Galaxies (UDGs), a galaxy population characterized by dwarf stellar masses but Milky Way sizes which is ubiquitous in dense environments and also detected in the field. We present a theoretical model for the response of dark matter haloes and UDGs to episodes of impulsive gas inflows and outflows. Assuming spherical symmetry, steady-state equilibrium away from the inflow/outflow episodes, energy conservation between shells enclosing a given collisionless mass and a transitional state in which the gravitational potential immediately adapts to the mass change while the velocities are frozen to their initial values, we predict the evolution of the collisionless density profile for a given instantaneous mass change. This model uses the Dekel et al. (2017) analytical parametrization of the collisionless density profile, for which we derive the local kinetic energy, but could be extended to other parametrizations. We successfully test its predictions on NIHAO cosmological zoom-in hydrodynamical simulations, showing that it is able to predict the evolution of both the dark matter and stellar density profiles between two simulation snapshots in a large majority of cases. This model thus provides a theoretical framework to understand both the transition from dark matter cusps to cores and the existence of UDGs.