As a person who loves apocalypse fiction I can think of many ways that a tiny minority of people can survive after a major die-off. It takes imagination but the solutions are there.
Assume that one out of a thousand persons survive and they start gathering together to live close together.
Telephone lines and power goes down since the people who supported the infrastructure are dead. Communication across town, state, country, etc is cut off.
Ham radios and walkie-talkies.
Oil refineries shut down, gas for travel starts becoming unavailable.
There would be thousands of gallons of fuel per survivor and the fuel at gas stations can become available when they are given electricity through means of generators. Any further transportation can be arranged by bicycles and any surviving horses. Keep in mind that people will be living close together in neighborhoods and have a lessened need for long distance transportation.
Crops dying in the fields, livestock used for milk and meat start their process of dying.
There is enough food in supermarkets to last every individual now living for 3 days. If one out of a thousand survive then there would be almost 9 year's worth of food as crops are planted. Of course Jehovah can arrange for a few farmers to survive and feed the rest.
Manufacturing of replacement parts for automobiles gone.
Go to Cuba and see how 1950s vintage cars are kept running without any factory made replacement parts. Besides, there would be over a hundred vehicles per survivor at a .1% survival rate.
Read Stephen King's book The Stand to get an idea of how a few thousand people can reclaim one city.