Production follows demand, always, no exceptions.
No demand (ie, no consumption) = no production, no investment.
Capital does not do "work" by any sane definition of the word. It enables work, yes, but that's quite a different thing. And still, capital only enables work when it's actually invested...and it's not invested without demand...and there's no demand without consumption.
And of course savings is the opposite of investment; It's the hording of capital, removing it from circulation.
Here's the real kicker: It really doesn't matter if anyone has savings available to invest in production...if there's demand, the market will find a way to meet that demand. But when there's little demand...? No level of savings will inspire investment or production.