The cyclical rate of unemployment can be negative, which implies that the business cycle sometimes produces too little unemployment. How can there be “too little” unemployment for the health of the economy?
Let me answer a simpler question first. Is it possible for there to be too little orange juice in the grocery store? Definitely.
Let's say that the price of OJ is set too low (\$1 per liter) and customers who arrive early in the morning buy all the OJ. Assume that those customers think buying all the OJ is a good deal and they figure they'll enjoy drinking it, but that at regular price (\$4 per liter) they'd buy much less, they wouldn't want any more at those prices, and there would be lots left on the shelves.
People who arrive later in the day want some OJ at \$4 per liter. If they could find them, the early OJ buyers would happily sell them the OJ at that price and pocket the profit (that follows by the demand schedule I sketched out in the second sentence of the last paragraph). That means that there are deals to be done that would improve the allocation of OJ (there are welfare increasing, Pareto-improving, trades to be made). But the early customers and the late customers have trouble finding each other and so the OJ stays in the early shoppers' refrigerators.
Just about everything I just said about OJ holds for worker labor. Surprise! If the price of labor is set below the equilibrium price then early buyers purchase an inefficient quantity. Later buyers can't find the workers they need even though the marginal value of those workers is higher than the price at which the early employers bought them. Because (or perhaps I should say if) it is less efficient to look for a job while you have a job, when unemployment is too low workers ended up employed by firms that do not employ them at their highest marginal product. If only alternative employers could be found output and welfare could be improved. In fact, using a Kaldor-Hicks mechanism it is possible to make the new employer, the old employer, and the employee all better off under such circumstances. Thus it is not efficient under production efficiency or welfare efficiency criteria.
Think of unemployed workers as a pooled/shared resource. Over the progression of the business cycle (economic expansion/contraction), business add to and draw from this pool as needed.
When cyclical unemployment is positive and high, unemployed workers linger in this pool for a long time, as job opportunities are hard to come by. Businesses have their choice as to whom they hire, for the worker pool is quite large, and workers have little leverage in the terms of their employment, as labor is plentiful. This situation would arise during the bottom of a business cycle, when the economy is contracting and/or just beginning to recover/expand.
When cyclical unemployment is positive and low, workers move out of one job into another with relative ease, staying unemployed for a relatively short amount of time. Business can add employees at will, though workers can now demand a small premium for their labor, as their particular skill set is harder to find among the available workers. At this point, the economy is firmly on the upswing and growing.
When cyclical unemployment is negative, workers move directly from one job to another without being unemployed. Additionally, businesses experience underemployment, that is they have fewer workers than they want. Labor commands a large premium, as businesses must steal workers from one another in order to satisfy their employment requirements. The business cycle is peaking, and the deficit of available labor will soon work to slow growth/expansion.
As usual in economics, the question is perplexing when considered from a purely quantitative point of view. However, once we admit qualitative variation, the answer becomes self-evident.
It is possible for there to be too little unemployment when there are too many "bullshit" jobs that do not create value and merely keep people busy for the sake of employment. Arguably, it would be better - and in aggregate cheaper - for those people to be unemployed.
We might venture to call this the "European model".