Prior to 1940, the money stock typically contracted significantly during a bust. People move toward holding currency by cashing out their checking account balances (or, in the 19th century, redeeming bank notes). The money stock shrinks as the bank money substitutes are eliminated.
After the Second World War, the money stock typically does not contract significantly during a bust. The Fed has manged to re-inflate during the bust by expanding its purchase of securities from banks. Even with fiat money, however, it is possible for the money stock to decline during the bust. It depends on the counter-veiling causal factors at work: the Fed’s attempt to re-inflate by expanding bank reserves versus people building cash reserves.
In my reading of the article, the author (p. 305f) is not suggesting what you’re implying. He is merely saying that when a catallactic offer is made it conveys only a promise and likewise with cratic offers.