Money is a funny thing.
When you pay out some money (when you "spend" it), the money doesn't actually get spent. That is, nothing happens to the money. It doesn't get consumed. It doesn't get worn out. It doesn't get used up. It just gets moved around.
When you don't pay out some money (when you "save" it), the money isn't actually saved. That is, it isn't saved from anything. Had you not "saved" it, nothing would have happened to it. It wasn't in any danger. It wouldn't have fallen off a cliff and died had you not "saved" it. It wouldn't have been consumed. It wouldn't have been worn out. It wouldn't have been used up. It has been saved only from being moved around.
That's not to say that moving money around doesn't do anything. It's a bit like electric charge. When electrons move around, there is an electric current, and things happen. When electrons sit still, nothing happens. But electrons don't get spent or saved. They just move around or sit still. It's the same with money. It doesn't get spent or saved. It just moves around or sits still. And when it moves around, things happen. People do things. Work gets done. Things get made. Goods get moved around.
It's not that nothing gets spent. Time can be spent. Energy can be spent. Fossil fuels can be spent. Resources can be spent. But money does not get spent.
Now, it does make some sense to say "I will spend some money" or "I will save some money". It means (respectively) "I have some money and I'm going to make it move around in exchange for goods and services" or "I have some money and I'm going to make it sit still for the time being".
But what does not make sense is to say "my scheme will save money" in an absolute sense. It might save me money, in that I can keep my money sitting still for the time being. But my cunning plan won't actually save money, because no money will be saved as a consequence. Money does not get saved.
So when, in the name of austerity, everyone tries to "save" money, what actually happens? No money actually gets saved. All that happens is that money moves around more slowly. People lose their jobs and end up sitting around doing nothing, supposedly so that money can be saved. But no money is actually saved.
It's a funny thing, money.