Perhaps you have heard about companies laying off workers here in the USA then having low wage workers in some other country do the work. This is usually called "outsourcing." But what if workers in the USA are employed by foreign firms? That is called "insourcing." According to the Organization for International Investment, we had 341,000 insourced jobs here in Texas in 2004 (only New York and California had more). I have not heard any complaints about the jobs Toyota has brought to San Antonio, where I teach.
No one knows if we have more outsourced jobs than insourced jobs. But what happens if there are more outsourced jobs than insourced jobs? Then our unemployment rate goes up. That, however, does not have to be a problem. If our economy falls below what we call the "full employment" GDP, the federal government can, as my students know, increase aggregate demand (AD) or the demand for all goods and services in the economy. This increases GDP, which means more workers will get hired since businesses that produce more goods, ceteris paribus, will hire more workers. So unemployment goes back down. In this case, inflation will not be a problem since the increase in AD happened with GDP being less than the "full employment" GDP (demand shifts to the right in a part of aggregate supply that is relatively flat, so prices rise very little).
If we tried to block outsourcing to protect jobs we would be blocking the gains and benefits we normally see from free trade. Many economists don't think that trade costs us jobs. But if just for the sake of argument that trade did cost jobs, we can get them back, using the policies explained above. Economists Paul Krugman and Douglass Irwin have made this agrument. Krugman suggests cutting interest rates as the way to increase AD.
For information on insourcing in Texas, see Texas is ranked third for 'insourced' jobs