If you remove power from the IC, any IC for that matter, and then apply an input signal, the behavior would be totally unpredictable.
What I have seen is, if the signal source has sufficiently low impedance and there is sufficient decoupling capacitance, the IC and perhaps other ICs, will continue to be powered thru the protection diodes.
But again......The circuit behavior will be unpredictable.
Whether the poor IC will survive the ordeal, that is a different matter.