What term is used for a US citizen or resident alien who lives and works outside the United States?

The term used for a US citizen or resident alien who lives and works outside the United States is "expatriate." An expatriate, often shortened to "expat," refers specifically to individuals who have chosen to reside outside their home country, whether for work, study, or other reasons. This term encompasses US citizens and resident aliens who have established their lives in foreign countries while still retaining their US citizenship or residency status.

In contrast, a foreign employee typically refers to someone who is not a US citizen or resident, but rather a citizen of another country working in the US or possibly abroad. The term "alien" is a broad legal term for a person from another country and doesn't specifically indicate their residence status or employment. The term "employee" simply denotes someone who works, without reference to citizenship or residency status. Thus, "expatriate" is the most accurate term for the specific situation described in the question.