your questions presume the existence of money^[1] and capital which can be held in private hands. by the time the state withers away, both will necessarily have been eliminated along with class distinctions. as capital is pure under the domain of the administrative apparatus and under democratic control, it cannot be used to accumulate wealth in the sense of the term as we understand it under capitalism.
can someone decide to accumulate currency? absolutely. what good does it do them? not a whit - once capital passes entirely into the public domain, the function of currency is no longer to denominate the flows of capital but rather merely to facilitate trade, as it was before capitalism, and will again be after it.
the unique part, that which has never happened before, is the social productive capacity of the whole society will lay entirely within the hands of the public at large - ie the ability to organize production without the interposition of private individuals, except where the production itself involves them materially.
[1]: money is distinguished from currency by the MCM’ relation, whereby money is turned into commodities through the process of production and the sale of said commodities becomes new money - ie profit. currencies by way of contrast have existed in many forms and for many purposes - I recommend David Graeber’s Debt for a survey.