The common pattern is that the off-shoring company will deploy workers on site for a year to do knowledge transfer and documentation of existing processes so that they can be moved off shore.
Usually (but not always) these workers come into the US on a H-1B visa.
I have not seen this in my career. Its usually PE or cost cutting causes US roles to be split into mult off shore roles because the pay per engineer is less outside the US. Like everything else the talent is a bell curve.
Nationalism and capitalism make uneasy bedfellows. Are American companies allowed to increase profits by selling abroad, but not allowed to employ abroad? That suggests that foreigners can't sell their skills to the USA.