There is a golden rule to live by: never invest what you cannot afford to lose.
FOLLOW IT.
This ^^ a million times over!
Let's say you are cannot afford to lose any of your savings so you don't invest anything then you have all your savings in fiat currency, investing in a currency that will lose its value over time
Your logic is flawed. The value of fiat savings actually generally will increase over time even though the principle will experience inflation as both investment returns and interest on bank savings generally will be greater then inflation.
No your logic is flawed. Having fiat is one type of investment where if state fails so does your fiat.
Investing in a bank is another type of risk. The reason you get the 1% from the bank is beause of the risk that the bank goes bankrupt is about 1% per year.
When you put money in a bank its a double investment as you will lose money if either the bank or the fiat loses value.
Fiat savings will get smaller purchase power with time as the state will print more money, this is money 101 really.
If you invest in a US bank then this logic holds up. It is generally accepted that the US is not going to fail. Also the US has FDIC insurance that protects depositors from bank failures
First of all a US bank can fail, many have, if the government decide to pay back depositors because they are not enough funds to pay them back in the legal order of repayment of creditors, they will inflate the currency so everyone will be poorer; the same will happen when the government inflate the currency to pay its obligations
Second of all banks in Europe start to have a negative interest rate meaning you are charge a % of your balance for the "benefice" of having it in your bank account
Finally, the FDIC only has a balance allowing to repay about 1% of the insured deposits of 250k of less; if you take into accounts deposits of more than 250k$ it is way less :
"A March 2008 memorandum to the FDIC board of directors shows a 2007 year-end Deposit Insurance Fund balance of about $52.4 billion, which represented a reserve ratio of 1.22% of its exposure to insured deposits, totaling about $4.29 trillion." (wiki)