This is sometimes called fountain pen money and it usually not disappears money but is how new money is created.
Banks can create new money with a proverbial stroke of a pen, lend it out and when the loan is paid destroy it again.
The bank of England has a pretty honest flyer about it.
A quote specifically about this misconception:
When households choose to save more money in bank accounts, those deposits come simply at th expense of deposits that would have otherwise gone to companies in payment for goods and services. Saving does not by itself increase the deposits or ‘funds available’ for banks to lend. Indeed, viewing banks simply as intermediaries ignores the fact that, in reality in the modern economy, commercial banks are the creators of deposit money.
The total absurdity of this situation, is that its very common for such loan to be paid off with a new loan, which is called “refinancing”