In this paper, we consider the sufficient and/or necessary conditions under which responses of unstable plants with zero initial conditions would be bounded under step inputs. Several possible unstable pole patterns are examined, and corresponding criteria are derived. It is shown that an unstable plant can be stabilized to have bounded responses using an alternate step input sequence. Step inputs simulate the saturated inputs in a feedback system with bounded control, where the closed-loop stability of an unstable plant is really difficult to study. Results from this open-loop study may lend some insight into the analysis and design of such feedback systems under input saturation nonlinearities.