The question is not ownership of jobs, the question is ownership of the market, specifically what laws must one abide by in order to trade in a particular nation’s market. We do not currently live in a borderless world, so the nation that allows its marketplace to be harmed via siphoning off money, job experience, etc. to other often unfriendly competing nations is a foolish nation indeed. Not only will their economy drain like an engine with an oil leak, say there is WW3 and massive cyber attacks are launched, and, oh darn it, no more American network security people, oops!
The economic genius of the USA is the borderless nature of the sovereign states. Workers, products, services and money are able to move with relatively few obstacles. This is one of the things that makes the US strong.
Suburbs were cheaper to do business than cities. So the market moved to the suburbs. Right-to-work_low-tax states attracted the market from high-tax states.
Opening the border to Mexico and Canada is similar. It makes for a stronger N America.
Curiously, the same people who oppose open immigration also opppose jobs going to Mexico... and Asia. The reality of the marketplace is that open immigration reduces jobs leaving. And closed immigration pushes more jobs to leave.