The phase separation behavior of intrinsically disordered proteins (IDPs) is thought of as analogous to that of polymers that undergo equilibrium lower or upper critical solution temperature (LCST and UCST, respectively) phase transition. This view, however, ignores possible nonequilibrium properties of protein assemblies. Here, by studying IDP polymers (IDPPs) composed of repeat motifs that encode LCST or UCST phase behavior, we discovered that IDPs can access a wide spectrum of nonequilibrium, hysteretic phase behaviors. Experimentally and through simulations, we show that hysteresis in IDPPs is tunable and that it emerges through increasingly stable interchain interactions in the insoluble phase. To explore the utility of hysteretic IDPPs, we engineer self-assembling nanostructures with tunable stability. These findings shine light on the rich phase separation behavior of IDPs and illustrate hysteresis as a design parameter to program nonequilibrium phase behavior in self-assembling materials.