If oil became worthless (hard to imagine), then much (but not all) of the middle east would fall into extreme poverty.
The rich would flee, the poor would starve. Their militaries would crumble from lack of foreign maintenance support (which is all that keeps them together).
The people would turn on each other and it would become one big Somalia.
Turkey or another Islamic power (not dependent on oil) might then step in to reconstruct the Caliphate over a weak and miserable population.
Of course, if the West didn’t close the door, they WOULD flood into Europe, trying to survive. What better target than the European welfare states.?
If oil became worthless (hard to imagine)
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Not really. However it would never become worth zero, just worth very little compared to today.
Advances and discoveries in natural gas and nuclear would do that very easily. If every country starts fracking for nat gas and starts building thorium reactors, the mid east would go broke very fast.
But over-run europe? no, europe would not allow that. They would over run africa first. Africa has raw materials and slave-like labor and lots of ground for farming. Africa would be the logical path for arab nations to save themselves from starvation. If there is to be a war as a result of the arabs becoming poor and going hungry, it will occur on the african continent.