"Withering away of the state" is a Marxist concept coined by Friedrich Engels referring to the idea that, with realization of the ideals of socialism, the social institution of a state will eventually become obsolete and disappear, as the society will be able to govern itself without the state and its coercive enforcement of the law.

Who asserted that the state would ultimately wither away? Let's have some stream of consciousness first.
To answer the question, consider the following: "Withering away of the state" is a Marxist concept coined by Friedrich Engels referring to the idea that, with realization of the ideals of socialism, the social institution of a state will eventually become obsolete and disappear, as the society will be able to govern itself without the state and its coercive enforcement of the law. So, the answer is Friedrich Engels.