If it in effect doesn't exist, then the rest of the money in circulation is worth more due to its scarcity being increased. Net economic activity is thus unaffected.
I've always seen this as an over-simplification that leads down an incorrect path of thinking. It "doesn't exist" if you think the only thing that has an effect on the economy is the number of dollars in circulation at a given instant. A person that has money saved may behave differently in the economy vs that same person with no money saved. They may buy different things or take bigger financial risks with the money they are spending.