  We generally study whether or not the information of an open quantum system
could be totally erased by its surrounding environment in the long time. For a
harmonic oscillator coupled to a bath of a spectral density with zero-value
regions, we quantitatively present a threshold of system-bath coupling
\eta_{c}, above which the initial information of the system can remains
partially as its long time stablization deviates from the usual thermalization.
This non-thermal stabilization happens as a non-Markovian effect.
