I am sure that it was not your intention, but please do not spread misinformation about the concept of natural rate of unemployment.
You are right that there will always be some unemployed as people need to find the next job after a surprising layoff. However, this is known as frictional unemployment, and can basically not be more than 2%. In practice, you'd expect it to be well below 1% in an otherwise well-functioning labor market, though I will admit that it depends on the exact institutions and laws surrounding labor.
What economists mean when they say "natural" unemployment is something else entirely. It refers to the (contested) idea that there is some "natural" rate of unemployment that the economy "wants" to achieve, in the sense that you will supposedly see some unintended negative side-effects if you use policy (such as classical demand policies) to push unemployment below that level. This unintended negative side-effect is typically said to be inflation.
There is some truth to this idea; the criticism is mostly in how one responds to it. There is truth to this idea because low unemployment increases the wage bargaining power of labor, which may result in higher inflation via the wage-price cycle.
However, the standard reaction to this is disappointing: Central banks purposefully generate unemployment to keep inflation low, making unemployment a macro-level problem, while the rest of policy (and public opinion) acts as if unemployment were the fault of the individual. This is clearly schizophrenic behavior.
The more intelligent response is to say that infinite demand for labor should be created at a fixed wage. This eliminates unemployment without enabling the wage-price cycle. This idea isn't exactly new, but it is not yet widely known, even though its supporters come from a surprisingly wide range of the political spectrum (the supporters disagree on the how of the implementation details; the main search keyword is "Job Guarantee", though I have also seen some superficially quite different proposals such as this one: http://www.morganwarstler.com/post/44789487956/guaranteed-in...).
Why is it not widely known? I believe it is a combination of (a) efforts to make this idea known outside of small academic circles are relatively recent, and (b) while individuals clearly benefit, there are no truly powerful individuals or social institutions that clearly benefit, hence the advocacy is not as well-organized as e.g. Austrian propaganda.