In what kind of economic environment would the cliche of "keeping money under the mattress" be warranted?
A fractional-reserve bank typically creates a lot of value by lending out your money to people while you are not using it. If you decide to take out your money on any given day, your dollar might not be there, but if not, someone else’s is! The bank will give you their dollar and wait for yours to come back from a loan.

However, during a bank run, many loans are going to default. So your dollar might not make it back, and if you’re not quick, you can’t take out someone else’s dollar cause they already got it back. Therefore your money could disappear.

No one can come into your house and take your dollar out from under your mattress though...