You don't save money by sitting on cash because your money is losing value rather than gaining it.

If your currency is deflating, usually that comes with a significant lack of confidence in markets. It takes an incredible amount of deflation to make investing a worse idea than hoarding - your currency would have to have become so incredibly scarce that the increasing demand for it outpaces real value of business productivity - but in the general case you are always making an informed choice between your money being secure - and the safest it can be varies by country. In the US, it is probably safest in an FDIC insured account, because you are more likely to have a safe in your house stolen and broken into than the bank and US government collapse in a way where FDIC insurance fails. But that is only 200k per account. There must be a threshold in any system where you stop insuring money - where you stop guaranteeing its safety - and you have to take that safety into your own hands.

In general, the least safe store of money is investment. Your investments could gain or lose all their value overnight, so it is risky. Next up is mutual funds, investment accounts, etc - ones that use the same risky pool but sample the whole thing to try to normalize the risk across the entire market. But entire markets can, and do, tank. Then you can put it in a bank - barring insurance, you are then trusting the bank not to go insolvent (through fractional reserve, which has the same investment connotations shares do), like they did in the great depression. If you don't have state insurance, bonds are often safer than banks because you are hedging against a countries solvency. And finally, you can keep it on your person - as long as you can keep yourself safe and secure, you can hopefully keep your money safe and secure.

In deflation, the fear is that the first three metrics of money storage lose their profitability potential sufficient to drive wealth holders to instead take money out of the economy and into their own safes. This drops the real money supply, and causes a deflationary spiral and more money leaves, money becomes scarcer, and people hoard more money. The endgame is that the currency stops working, because people start treating it like gold rather than a means of exchange - you hoard it because it is worth a lot, but you do not want to spend it because it will probably be worth more tomorrow.

The inverse problem is an inflationary spiral, where a money supply is seeing such an extreme glut of money entering markets that people are selling all of it off to try to offset its lost value, which perpetuates the drop in value. Unless it is backed by material goods (fiat moneys are not) inflationary spirals, uninterrupted, end at a worthless currency - nobody wants any of it because nobody thinks it is worth anything.

Governments create inflation to offset deficits, surely, but they also create inflation to avoid either scenario. But in general, inflation increases monetary velocity - the more inflation you have, the more value holding the currency you lose day over day, and thus the more pressure for you to get rid of it as fast as possible before you lose more value. You want to walk a tightrope between where people do not want to keep it and where people do not want to receive it, but usually low amounts of inflation are sufficient to get almost all money moving without compromising much confidence in its buying power, hence why every modern economy targets similar 1%ish inflation levels.

Deflation, on the other hand, slows down the economy by driving the desire to not spend money. Even 0% inflation - when the currency is simply stagnant - can be disastrous for an economy because it suddenly changes the game from "I have money and its worth less every second" to "I have money and it will be worth the same / more tomorrow than it is today". That can cripple economic cycles necessary to sustain countries.