If the company does hire an already-employed person, isn't that person's previous employer likely to look for a replacement? If the total number of jobs increas

If the company does hire an already-employed person, isn't that person's previous employer likely to look for a replacement? If the total number of jobs increases by one, the total number of unemployed people should decrease by one. This seems like a way for one company's HR department to offload some of their work to another company's HR department. Of course, the added cost of training a new worker might mean that the previous employer does not replace the employee.