If businesses always strive for productivity improvements and we only expect new jobs to come from the business sector, then yes, we will always have unemployment.
And since businesses should always strive for productivity improvements, then the only way to limit unemployment is to find a way to employ the workers that aren't needed.
I can't say that unemployment is what causes the riots, I was only responding to what you'd said earlier. Rioting is generally counterproductive, but it's also rarely as simple as "street thugs running wild". Frustration and youth are a dangerous combination.
As long as there's economic growth there will be an infinite stream of new jobs as new businesses are created and operations are expanded. Increases to efficiency, say to automation, might eliminate one job, but at the same time create another industry of jobs to build the automation. In general, the money freed up from increased productivity get invested and create new jobs someplace else.
Full employment is not possible simply because there is always X percentage of people who are between jobs, or get caught in some entitlement trap, or aren't employed for some other reason.