"...it may be doubted whether under a system of barter the decisions of individuals would have their full effects..." - Piero Sraffa (1932)In the General Theory, Keynes presents an argument for how widespread unemployment can come about. I think money enters in an essential way in Keynes' argument. This raises the question whether unemployment would exist if it were not for monetary phenomena.
Sraffa, in Production of Commodites by Means of Commodities, has a lot to say about numeraires, including the Standard Commodity. One can read Sraffa as making certain points about a monetary economy.
But put that reading of Sraffa aside. Instead, think of Sraffa's model as half of a limit point of a neoclassical model of general equilibrium. The other half of such a model of a steady state consists of utility maximization. This is a model of a barter economy. And steady state models can exhibit multiple equilibria, bifurcations, and catastrophes. I think these phenomena suggest the possibility of complex dynamics. Thus, even though neither general overproduction nor an uncleared labor market can arise in a long run competitive equilibrium in a barter economy, such an equilibrium may never be reached. Instead, the economy may cycle around with unemployment continually being recreated.
The idea that unemployment could be cured by making labor and product markets more flexibile is unsupported by price theory.