Can a persons money wage decrease at the same time their real wage increases?

Yes, a person's money wage can decrease while their real wage increases if the rate of inflation decreases faster than the reduction in their nominal wage. For example, if a worker's nominal wage drops by 2% but the inflation rate falls by 5%, the purchasing power of their earnings—real wage—can increase despite the nominal wage decrease. This situation highlights the distinction between nominal and real wages, where real wages reflect the buying power of income adjusted for inflation.