For many classes of occupation, American work visa belongs to the company that's employing the foreign worker, and are valid for that person only while they are in the specific position. There are rules about the "need" to have a foreigner in a given position, as opposed to an American citizen. The employee is not free to resign and just hang around in the States, or change jobs at will, unless they have, on their own merit, obtained a regular green card. I know this because a close relative was in the situation. He got his own documentation when he knew the original position was winding down, and now owns and operates a small business. He's been married to an American for 20 years and both his kids were born there. While it's unlikely he'll ever come back to permanently reside in Canada, he has no plans to take US citizenship.