First off, I'm not sure you can classify Marx's communism as a "social order"; Marx is envisioning a systematic failure of capitalism as a cohesive institution and pontificating about what might come in its wake. Because Marx doesn't believe that change happens "naturally" but only in violent upheavals, he thought "now is the time for a new social order!" in his own context, sure, and supported a Communist Party, but his analysis in Das Kapital is much more about the failure of capitalism with the increasing mechanization of the means of production.
The point is basically that Marx wants to start every social analysis by asking, "OK, in this society, who is the slave class? And who are the people who own them?" Marx saw that industrialization was increasingly multiplying the capabilities of this slave class, and indeed supplanting them. Marx envisioned that eventually, the slave class would entirely consist of robots of one form or another, with the only humans entering being the ones who voluntarily wanted to do that sort of work -- sort of the model of the CEO who leaves his cushy job because he wants to be a farmer at heart.
It's a very techno-utopian vision of the world, and it's hard to see what the social order that lives atop this is going to be. Marx famously extrapolated that the control of the 1% over the 99% was going to persist into this technological switchover, and that the 99% was going to realize it and lead a revolution-to-end-all-revolutions, because afterwards there would be born a society where every human was guaranteed the basics of everything they need (by the robot slaves and the volunteer slaves) and could pursue whatever artistic calling suited them.
But that remarkably underspecifies the nature of the underlying state, of course. The "nation with no state or laws" is one possibility, an anarcho-communist vision, but there could also be a normal modern constitutional republic, where there would be the normal boundaries in place preventing people from gathering the resources to take over the nation. It's rather hard to say.