The fact that the money is "created" and "destroyed" is the nature of the Fed. They don't need to have money in order to lend it. That's what the Fed is.
These loans are literally the same as printing money, loaning it, collecting the loans, and destroying the printed money. Except everything is just numbers on a balance sheet, so no physical money needs to be physically printed or shredded. The effect is still the same: The Fed decides that money should enter the money system, and also describes how that money will leave the money system.
when the fed receives a check from a bank, the money doesn't get deposited and stored in some account, the money just stops existing.
terms to google: "monetary policy", "open market operations"