Society won't collapse. Humans will do amazingly evil things to survive. The British were happy to starved millions of Indians to death until the country gained independence. All to support the British empire. We live in an era of basically unprecedented niceness in the history of humanity. Even the great empires of the past oppressed and killed multitudes more through slavery or serfdom or constant expansionist wars or other such means.
> refurbishment of houses
Perfect work for refugees to do at gun point.
Billions may die but society will go on with a somewhat lower regard for life and a larger amount of nationalism. Arguably what we consider western society will collapse but that's only existed for under a century.
In some ways that is more depressing than society simply collapsing. We will leave behind a rotting zombified corpse of our society to future generations.