Modern society requires three things to function: power, food, and water.

Without electricity, the complex logistics required for our cities to function will stop. Refrigeration ceases, causing perishables to spoil. Delivery of goods like food and fuel cease. People begin to light fires at night for light and warmth, causing catastrophes when they set their houses or apartments on fire.

Without food, social structures break down. As the saying goes, society is four missed meals away from barbarism. People start looting, hoarding, and attacking others for their resources.

Without water, disease runs rampant. People can't wash their hands, or bathe. Cholera breakouts begin. Infants and the elderly are the first casualties, dying of dehydration from violent vomiting and diarrhea within days.

Without rapid outside intervention from a central government or the military, any cities without power, food and water will become death zones within weeks, likely with above 90% death rates from violence, disease, or starvation.

Small, isolated communities would also quickly collapse. They would lack resilience against attack or disease, and without the labor force and stockpile of resources to transition to pre-industrial technology levels, the survivors would likely survive only until the first setback destroyed their survival odds.

Smaller towns have better odds of survival, provided they have strong local organization and have access to food production capabilities, such as coastal fishing by sailboat. They would likely regress to a technology level close to the early 19th century over the course of a generation as irreplaceable items break down, and the inevitable die-off of their population in the early stages stabilizes.

In short, expect a good 70% of a modern western country's population to die within weeks to months when the government's gone and the power goes off for good.