No, when the price level falls, the value of money does not fall. In fact, the reverse happens. When the price level rises, the value of money falls. When the price level falls, the value of money rises.
An increase in the price level is called inflation. When inflation occurs, money loses its value. This makes sense because an increase in the average price of everything means that each dollar does not buy as many things as it previously did. This is a major reason why our salaries today are astronomically higher than they were 50 years ago. We are richer in relative terms, but part of the reason is that everything we buy costs more in absolute terms than it did then.
A decrease in the price level is called deflation. When deflation occurs, money gains value. If the prices of all the things we buy go down, each dollar that we have is suddenly worth more. We can buy more with a given dollar than we could have previously.
So, the question has it backwards. When the price level falls, the value of money rises.