Just existing doesn't give them value. After an apocalypse event, even with some sort of US military and US government functioning dollars will lose their fungibility quickly. What could happen is an increased supply of them e.g unprotected banks/vaults could be robbed. But this would have the effect of making more dollars available, so although they exist they are not scarce, if they are not scarce then why would I swap them for 10gallons of fuel? ATMs would be easily looted and are widely located.