Helium is produced from natural gas wells but with the prices for the gas where they have been for so long no one bothers to capture it - it's not worth it, it's just vented to the atmosphere and escapes.
So "running out of helium" basically means "running out of cheap helium and the price will go up until it establishes a balance with the cost of producing it from the ground instead of a government storage tank".
For as long as we get natural gas out of the ground, we will have helium.