The first example that comes to mind is the textile industry starting in the northeast US where unions are strongest, then moving south where they still had some unions but were much weaker, and eventually going overseas. Could argue the same thing for the US steel industry but I don't know. Or you can also find plenty of companies keeping their legacy business with unions as they are but only expanding forward to places not so friendly to unions - e.g. Boeing opening its latest plant in South Carolina without a union unlike its original counterpart in Seattle. Of course there's already differences in labor costs regardless of unions and other factors at play.

I'm for unions in principle and I have family members that have certainly benefited from unions on the one hand but I've known plenty of people in private sector unions that feel like their union dues are only getting someone else richer while they're stuck in dead-end jobs just to make ends meet.

Some union contracts actually let the union veto the outsourcing of jobs.

In those cases unionizing prevents outsourcing.

My phone company sent a bunch of call center jobs to the Philippines… it’s not really a talking point or anti-union to say that businesses will at least consider alternatives.