equilibrium - Why is it valid to assume that the liquid-vapour interface is always saturated during evaporation?

For steady state evaporation, I read from two textbooks which simply states that the partial pressure of vapour of interest (say water) at the liquid-vapour interface is equal to the saturation pressure of water at the interface temperature ($P_{sat}(T_{interface})$)? I am wondering why steady state evaporation cannot be established with an interface vapour partial pressure lower than $P_{sat}(T_{interface})$?