The Trump administration will now require people seeking green cards to leave the United States during the application process — a sweeping change that could upend the lives of hundreds of thousands of people seeking the right to legally and permanently live and work in the US.

Most applicants already living in the US will now have to leave the country and apply from their home nations.

While there are approximately 1.5 million Indian Green Card holders in the US, an additional 1.2 million highly skilled Indian nationals and their dependents are estimated to be presently stuck in the...