Money you deposit in a bank is guaranteed by the state up to a certain limit (often 100 000€ per person per bank).
Source (french) : https://www.ecb.europa.eu/ecb/educational/explainers/tell-me...
> Selon la réglementation européenne, ces systèmes assurent 100 000 euros par déposant. > (DeepL) According to European regulations, these systems guarantee 100,000 euros per depositor.
> If you have $10,000 then you have $10,000.
Playing devil's advocate: that's as long as the denomination doesn't change. Once it changes (for instance Cr$ -> NCr$ -> Cz$ -> NCz$ -> Cr$ -> CR$ -> R$, and I lived through most of these changes), and you're outside of a conversion grace period (when you can take your cash to a bank and exchange it for new notes), your cash is worthless; if I find an old Cr$ bill stashed somewhere (I probably still have some), they're not worth much more than the paper they're printed on. If your money is in a bank, on the other hand, it will always be converted automatically and transparently.
(On the other hand, I also lived through the infamous "confisco da poupança" which froze most of the money in everyone's bank accounts, so I can clearly see the importance of having money outside of the reach of banks. On a third hand, I also lived through the hyperinflation times, and know that having too much of your money not deposited in an interest-bearing bank account or other similarly good investment means it will lose its value quickly.)
If you have $10,000, then you have $10,000.
If you deposit $10,000 in a bank, then you have $0 and a promise from a bank that has $1,000 and a promise (from somebody else) for $9,000.