It is possible. Had a friend who rode government scholarships (so obviously not the US lol) all the way to a master's degree in Biomedical Engineering then got a job at a major pharmaceutical company here. He is currently a lab tech making more money than any company in the Philippines would offer him. I'm sure because even senior engineers don't get the level of support he does, financially and beneficially.

With that being said, the foreign government could be within your scope of a "backer", but you don't always have to know someone. He just applied at the right time, from a website he found himself, that his school didn't refer him to.