Why does this need any reconciliation? That's working as expected: when productivity improves in some sectors, we don't need as much labour there as before, and thus it needs to be shuffled around. This can have all kinds of knock-on effects.
As long as central bank is doing at least a halfway competent job, overall unemployment will stay low and stable. Ideally, you have people quit for a new job instead of getting fired, but in the grand scheme of things it doesn't make too much of a difference, as long as in aggregate they find new jobs.
An interesting example is furnished by the US between early 2006 and late 2007: hundreds of thousand people left employment in construction, and during that same period, the overall US unemployment rate stayed remarkably flat (hovering around 4.5% to 4.7%). The US economy was robust enough to handle a housing construction bust.
(Of course, after this was all done and dusted, some people declared that house prices were too high and the public demanded that they be brought down. So obligingly in 20008 the Fed engineered a recession that accomplished exactly that..)