If a resource is truly nonrenewable, the world will have to (by definition) run out of it eventually if the resource is being heavily used relative to how much of it there is in the world. By definition, if you have something that cannot be renewed and you use it, you will eventually run out of it. The question is how long this will take.
For example, we will clearly run out of oil someday. However, we really do not know when this will be. There was a time when the “peak oil” hypothesis argued that this date would arrive relatively soon. However, this no longer appears to be the case. This is because technology has improved and allowed us to get at more oil for a lower price. In addition, the ability to get at natural gas through “fracking” has greatly lowered the amount of oil that needs to be used.
What this means is that we are no longer likely to run out of oil any time soon. But we will still run out someday if we continue to use a lot of oil. You cannot use a finite resource without running out of it at some point.