If money expenditure on output increases, then firms sell more, produce more, and employ more workers. Real wages remain unchanged. The surplus of output and the surplus of labor disappears.
If, on the other hand, money expenditures remain depressed, there is a market solution. The usual response to a surplus is a lower price. The surplus of labor leads to lower wages. As prices and wages fall together, real wages remain the same. However, if money expenditure on output remains the same, the lower prices result in higher real expenditures on output. Firms produce more and hire more labor. The lower money wages were essential to keep real wages from rising and depressing employment.
Note that real wages play no role in either process. Employment fell, and unemployment rose, without real wages changing at all, much less rising above equilibrium. Similarly, an expansion in the money supply increased output and employment without lowering real wages or impacting prices or wages at all. And finally, even if nominal expenditure remained lower, and both prices and wages fell in response to surpluses, employment recovers without any decrease in real wages.
So why is there a tradition of focusing on the real wage? In microeconomics, the demand for labor depends on the real wage. But then, everything in microeconomics is about relative prices, and that includes the relationship between the price of labor and the products of labor.
In macroeconomics, the reason for the focus on real wages is an assumption that wages are sticky and output prices are flexible. If nominal expenditure falls, then as explained above, the demand for output falls. As firms sell less, they lower prices. This raises real wages, and reduces the quantity of labor demanded and raises the quantity of labor supplied. The result, then, is a surplus of labor. Of course, the increase in real wage is also an increase in real costs, and so firms produce less. So, the result of the decrease in nominal expenditure is lower prices, lower output, lower employment, and higher real wages.
If money expenditure increases again, then prices rise, real wages and real costs fall. Firms hire more workers and produce more output. Recovery through an expansion of money expenditures requires a price increase and lower real wages.
The market process that corrects the disequilibrium is lower money wages. This reduces real wages and real costs. The firms hire workers and produce more. To sell the extra output they lower prices. Given nominal expenditure, real expenditure rises. Firms can sell the additional output.
Market oriented economists have sometimes ridiculed the notion that increased nominal expenditure can raise employment. If workers will continue to work (and return to work) in the face of increase nominal expenditure, higher prices, and lower real wages, then why don't firms just cut money wages, reduce prices, and reduce real wages? It must be money illusion.
I don't pretend to have all the answers as to why money wages are sticky. However, the notion that reversing a decrease in nominal expenditure and a temporary decrease in output prices, would cause workers to do anything other than mourn the loss of the remarkable bargains they enjoyed for a time is absurd. That they would demand a nominal wage increase to permanently capture the transitory increase in real wages is possible, but not likely.
Is that money illusion? I don't think so.