Saving money amounts to producing some wealth without consuming any wealth in exchange (generally because you expect your savings to conserve value, and therefore get the right to consume without producing some time later. Like all bets and promises, sometimes it works, sometimes it doesn't)
That's good for the economy when there is a lack of supply: plenty of people willing to buy stuff while nobody wants to make those stuff. When there's a lack of demand, it doesn't help. When there's a lack of demand, you need to make people consume more, possibly by delaying / alleviating the expectation that they produce something valuable first. This consumption is expected to allow creation of supply. That's the principle of a Keynesian stimulus.
The problem typically associated with massive unemployment is a lack of demand: there are plenty of unemployed people who would like to produce and consume, but they can't find anyone willing to buy whatever they might produce.
Put another way, UBI is a way to raise the velocity of money, the amount of commercial exchanges per amount of time occurring in the economy; saving lowers money velocity.
> money "saved" is usually invested, and that too stimulates an economy -- and probably more meaningfully long-term.
Money gets very tricky at scale. If "money" means "paper bills" and "saved" means "sitting in a warehouse", then no, saving enormous amounts of money will not make you richer or improve your future. You can't eat bills—or bitcoins. And indeed, if enough people decide to hold onto large amounts of cash, it makes it harder to trade.
Can this really happen? Sure. When the market looked like it was about to crash in 2008, I moved my investments out of index funds and into cash equivalents. Now, this might have been a dumb move—but I'm not the only one who panicked and invested very conservatively. As a result of this, it became much harder for even solvent businesses to get short-term loans to pay for inventory, etc.
Or we could use a really simple model to visualize this: Imagine that the entire economy consists of (vertically integrated) restaurants. When the economy goes to hell in a hand-basket, people will do two things: (1) eat out less, and (2) try to get more hours at work. Obviously if nobody eats out, the restaurant will not be offering anybody very many hours!
What's happening here is that a sudden change in risk tolerance drops the total demand for goods and services below what the economy is capable of producing, while increasing the number of people who want jobs. When demand is lower than production capacity, we'll produce less than we can, and fewer jobs will be available. Apparently, you need a reasonable balance between the number of people who want to work, and the quantity of goods we want to consume.
Now, is any of this true? Who knows. The Keynesians certainly think so, and their model does explain some things. (Krugman, who's a Keynesian when he's not a political commentator, gives his own personal favorite introduction here: http://www.pkarchive.org/theory/baby.html) Other economists disagree. And of course, it's also possible that the Keynesians were correct about the exceptional events of 1929 and 2008, but that their theory is irrelevant in ordinary economic times. But the key takeaway is that money is weird at scale—because it's basically an illusion, among other things—and that you shouldn't expect personal intuitions from your day-to-day life to always apply in obvious ways.
It logically leads to the existence of an optimum rate of saving/spending and the requirement of some powerful actor to keep that rate near optimum. Notice that the math is flawless, but there are some issues with its meaning, so again, reality is more complex than that too.
i read this all time around here. money "saved" is usually invested, and that too stimulates an economy -- and probably more meaningfully long-term.