The Federal Reserve can indeed unprint money....
...
They did so on a Monday in 1929
Don't confuse Federal Reserve actions with Market actions.
The Federal Reserve is not the only entity that creates money or that can destroy money. Every time a loan occurs, it creates money. Every time a loan is paid off or cancelled it destroys money.
That Monday you refer to was market action destroying dollars, although it was in response to prior tightening by the Federal Reserve.
Think money multiplier effects. So the Fed tightens money. Banks in response don't renew loans, refuse to issue new ones, or call in issued ones. Stocks fall, Brokerages call margin accounts (which are loans) stocks fall more. People panic and sell. stocks fall, more margin is called. People run on banks, banks call more loans. Vicious stuff.
But now the FED monitors that. Steps in making more liquidity available so banks can meet capital requirements stopping bank runs. No Fed = no chance to stop it. Depression. Failed businesses, failed banks, high unemployment, foreclosures, economic mess, soup lines.