Marx' reasoned position on this is that one could not know in advance. It would be something for the new workers' government to decide, and anyway Political Economy -- the economics of capitalism -- could not tell us anything about it. But Marx probably did have some ideas about it, and Marxists certainly have some ideas about it. We cannot quite dodge the question here!
Marx and Engels were very impressed by the factory system, but Marx was also impressed by the potentiality of cooperatives. He wrote, (Capital, v. III, ch. XXVII) "The co-operative factories of the laborers themselves represent within the old form the first sprouts of the new ... The capitalist stock companies, as much as the co-operative factories, should be considered as transitional forms from the capitalist mode of production to the associated one ... "
The founders of the Soviet Union took that as the basis to create a very centralized, and, in practice, bureaucratic system. The Communist state was to become "one great producers' and consumers' cooperative." (One could equally have said that it would become one great capitalist stock company!) We can now assess this view on its results. Didn't work.
However, some Marxist scholars read Marx closely and drew a quite different conclusion. Shirley Telford's ideas, from the 1950's and 1960's, may serve as an example. From Economic and Political Peace, (Portland, Oregon: William and Richards, 1969, pp. 2, 10, 16) "According to Marx' theory, there should be an associated control over production. ... As long as the individual works in a particular cooperative enterprise, he owns the means of production and profit of enterprise in common with the other members of the enterprise. ... Associated production is established by the conscious action of society, as a system of production that is understood by those who establish it. Its establishment is made possible by the dissolution of the capitalistic property relations." Telford's point is not so much to establish that this is a good idea (though she clearly feels that it is) as to establish that it is a Marxist idea, and here she succeeds. It seems clear that a system of federated cooperative enterprises has at least equal claim to the label "Marxist economic system" as the failed system of government central planning had, and probably a better claim.
To borrow the title of one of G. D. H. Cole's books, "what Marx really meant" will not be of interest to everybody. But this kind of Marxist thinking may be important to everybody, because it describes a system in which working people establish their own government from the bottom up. If government continues to collapse, we may have no choice but to do just that. When government is the problem and is collapsing, then it doesn't make sense to turn to government and say "Do something! Solve the problem." We have to do it ourselves. And, ironic as it may seem, it could be Marxism -- one kind of Marxism -- that can teach us how to do it.
What, then, is the future of Marxism? Certainly not in the failed Soviet system. But it will depend on the future of capitalism. If Marxism is right on the facts, capitalism will continue to be plagued with crises, dynamic but unstable, until the system of exploitation by employment for wages collapses. Some more highly evolved system will replace it, but perhaps not right away. We could be in for a long "Dark Age." That may depend on choices we make and actions and direction that we take. It's hard to be optimistic, though. On the other hand, if Neoclassical or Keynesian economics is right on the facts, then we needn't worry about all that. Business as usual can go on as usual -- perhaps with a little government tinkering.
Judge as best you can. Time will tell.
Here is more on cooperative enterprises and the possibilities for a socialist society based on them.