As with current Fed policy, there would be both winners and losers if the Fed did nothing. Either way, there will be pain, but without the Fed we'd actually build the foundation for a more sound and lasting economic system.
No matter what the situation, no one has the right to compel someone to act for another's benefit, and that includes forced quarantines, business closures, and expropriations of medical equipment in the name of "public health."
The idea that a free and mostly privatized society would let pandemics rage unchecked is based on a crude caricature. The truth is that a free society offers flexibility and resilience that a centralized system lacks.
Anti-price gouging laws mean that those who really end up getting the short end of the stick are those who don't have the time or the means to beat the crowds to the store. Worse off are those of lesser means who rely on public transportation or walking to transport groceries home.