Wasn't the question about the Monetarist solution? Monetarist is not Austrian even if they're both cited by conservatives.
The monetarist solution is to print money to keep the money supply from dropping, helicoptering it in if necessary. Milton Friendman is actually the source of the "helicoptering money" phrase, from his book "The Optimum Quantity of Money."
The Austrian Von Mises also said that after inflation, the government should avoid compensating deflation, although he was not so explicit about what to do with a liquidity trap. I'm not an Austrian expert, but Von Mises did advise the Austrian government, and he did often advise them to do things. "Do nothing" isn't an accurate assessment.