Numerous works have shown that under mild assumptions, unitary dynamics inevitably leads to equilibration of physical expectation values if many energy eigenstates contribute to the initial state. Here, we consider systems driven by arbitrary time-dependent Hamiltonians as a protocol to prepare systems that do not equilibrate. We introduce a measure of the resilience against equilibration of such states, and we show, under natural assumptions, that in order to increase the resilience against equilibration of a given system, one needs to possess a resource system that itself has a large resilience. In this way, we establish a link between the theory of equilibration and resource theories by quantifying the resilience against equilibration and the resources that are needed to produce it. We connect these findings with insights into local quantum quenches, and we investigate the (im)possibility of formulating a second law of equilibration by studying how resilience can be either only redistributed among subsystems, if these remain completely uncorrelated, or in turn created in a catalytic process if subsystems are allowed to build up some correlations.