If the situation lasts long enough, the standard of living falls.

Money exists to move goods around. If all the money is in one place, goods cannot move.

Money is not limited. It is an information measure of, variously, debts, or bidding rights to production. What it can bid on is limited, and how currency-denominated asset valuations change as money supply and circulation do, can also change.

But the problem in the case of a national disaster isn't that money cannot be produced. It's that those who would rely on money to address immediate needs (water, food, shelter, medical care, transport) have no bidding rights (currency, credit, grants) to transact purchases. You're balancing the interests of those outside the disaster zone (assuming there is an outside) with those in it. (Though this generally is the case.)

If the disaster is big enough, and rescue or infrastructure needs sufficiently high, those may affect national accounts and economic activity for a time, but it would take an absolutely massive shock for the impairment of raw productive capacity alone to impact the economy. Far more likely that buying power is lacking amongst a segment of the population.

And for that, money is precisely the cure.