In this work, we construct a time-dependent step-like potential supporting a normalizable state with energy embedded in the continuum. The potential is allowed to evolve until a stopping time t(i), where it becomes static. The normalizable state also evolves but remains localized at every fixed time up to t(i). After this time, the probability density of this state freezes becoming a Bound state In the Continuum. Closed expressions for the potential, the freezable bound state in the continuum, and scattering states are given.