There are a number of points that must be made here.
First, there are many people who would dispute the idea that outsourcing is a “problem.” To many people, outsourcing is an important business practice. It is a practice that lowers the costs incurred by companies and thereby lowers prices for consumers.
Second, not all “outsourcing” contributes to unemployment in the United States. Only “offshore outsourcing” has a major impact on unemployment. This is because outsourcing is simply the practice of having some aspects of a firms operation done by an outside firm, not within the company. In other words, outsourcing can happen within the United States. Any outsourcing to American companies does not tend to increase unemployment much.
That said, there is a link between structural unemployment and offshore outsourcing. Structural unemployment occurs when a particular worker’s skills are no longer needed in the domestic economy. Offshoring has resulted in the disappearance of some entire industries in the United States. People whose skills were needed for those industries (mostly manufacturing industries) became structurally unemployed because their skills were no longer needed in the US.
There is, then, a connection between structural unemployment and offshoring. Offshoring makes certain classes of jobs disappear from the US economy. This makes the people who did those jobs suffer from structural unemployment.