Bryan writes then when technological change occurs, we should observe
Cut wages in existing industries drastically enough to keep firms afloat and workers fully employed.
That is true for small changes. Mathematically, it assumes continuous functions.
It may not be true for large changes. Suppose that somebody brings a tractor to a farm, so that the farmer can do the work himself without the help of hired labor. The marginal product of the worker might now be below the subsistence wage.
Tyler Cowen uses the acronym ZMP to stand for Zero Marginal Product. The point is that new production methods can drive the marginal product of existing workers way down. Firms also face non-wage costs (e.g., health insurance) of retaining workers.
Even with discontinuous changes, the phrase "drastically enough" can be invoked to suggest that wage cuts could cure unemployment. But suppose that "drastically enough" means 25 percent or more. If you want to say that the PSST story of unemployment depends on wage stickiness because such a large wage reduction could take care of things, then fine. You have scored a debating point without practical significance.