The traditional way to look at keeping a stable employment rate, or at least when trying to attempt to move employment rate toward specific number, is by looking at the job finding rate and the job losing rate in an economy. When these two number are constant, all other things equal, the unemployment rate always tend toward equalibrium, or the natural unemployment. This is especially important because this model of the labor market show that the size of the labor market doesn't matter. Even in the event where there are constant influx of new workers into the labor force, which might result in what some European call hysterisis, the result still remain predictable. In such instance, even if there is not one specific point that the unemployment tend toward, it often move toward a predictable and observable band. This tell us that what matter is the rate of job finding and job losing rate in an economy, and it is controlling or adjusting these number that often have the best result when in come to unemployment.
However, that also mean that if a nation, like France, make it harder for people to lose their job, it would make it harder and slower for companies to find worker, which would mean that less people would be working. (Why, because if employment contract is hard to break, employer have to be more careful who they hire.) When trying to manipulate these numbers, careful positive analysis must take place for any policy that attempt such thing, else the result can be very counter productive. Just look at America, which lost about 90,000 job daily. Such number seem devasting, but if we look at the job finding rate and job losting rate for America; the job losing rate has been constant at about 1% for the last decade while the job finding rate has been increasing. The result is that America umployement has gone from an average 7-8% from the past to a good 4-5%.
Is that suggesting that for a nation that have a shrinking labor force - due to an aging population - they should support immigrantion as a way to reshape the population pyrimid, and rebalance the shape of the population? That could be a solution, however, there are something that we must pay attention to if such a policy is embrace. The above discussion show that influx into the labor force will not creates huge jump in umployment, and in the long run, it make no real different. But, we must pay attention here to the rates of finding and losing job. Influx doesn't matter under the assumption that it does not alter these important rate, but what if it does?
The best way to look at the labor market is through Schumpeter's creative destruction. In such a model, economy are always breaking down the old and building new to replace it, job are destroy to be replace by better more advance job. What would happen when the influx into the economy is behind the current technological state of the economy, and that they are so behind, it is impossible for them to catch up? If we denote influx into the labor force as theta, then we must have two different theta value, one that represent those that can be added to the economy, and one that will have to eventually give up and leave. In such situation, I would assume that the second theta value would have some motifier to the job finding rate as it is a whole group of people that have no chance of finding job at all. How big of an impact it will have, though, I do not know. Maybe in the long run, it is neglectable. But that is why economic analysis is for, and hopefully I can get some real number for this situation.
Now imagine another situation, what would happen in the model if we have a constant out flow of workers without inflow?