They live life without God. It’s not a new concept.
The idea of a “Supreme” God was invented by the Zoroastrians. Before them, peoples’ gods existed alongside other peoples’. Judaism elevated the idea further with the concept of ‘ethical monotheism’, which holds that all morality stems from God. So there’s that aspect. The whole concept didn’t have meaning until it was invented.
Christianity invented the concept of a God that was a deity for everyone. The Jews still believe that religions are necessarily regional. To be Jewish, you either have to be able to trace your lineage to an existing Jew, which presumably could trace theirs all the way back to ancient Israel. If it weren’t for the Romans scattering the Jews all over Europe by destroying their Temple, they’d still all be there. Anyone can be Christian just by accepting Jesus. To become Jewish takes work.
Jews believe that God can leave them. The Torah has many mentions of God leaving the Jews at various points in their history, such as when He led the Jews into being enslaved by the Egyptians, eventually leading to the Mosaic period.
Christians invert this by saying that you have to constantly open your heart to Jesus. It’s a conscious act to bring God into your life, something you have to do more and more over the course of your life. The idea of God leaving a Christian is unconscionable. It’s you that leaves God, God would never leave you.
What happens when you don’t have God? Well, you don’t have God. It’s pretty simple. What that means can vary, but it’s not as complicated as people often make it out to be.