Taking money out of circulation (by saving it/not spending it) reduces supply, practically speaking, raising its value, causing deflation (price levels drop, cash becomes more valuable). This isn't controversial, it can be seen in recent history. Expansionary monetary policy (increasing the supply of money) = inflation, deflationary policy (reducing money supply) = deflation.

> That doesn't make any sense. If the rich hoard money the velocity of money goes down, and that causes the value to go down too.

'Velocity' of money is a shitty concept, but regardless what it means is that with higher velocity, goods and services are in higher demand relative to cash (more transactions over time). This increases price levels but reduces the value of cash.

So velocity going down decreases demand for and the value of goods and services (price levels), increasing the relative value of cash.