Donald J. Trump’s foreign policy proposals, like forcing Mexico to pay for a border wall or withdrawing from NATO, have drawn unprecedented condemnations as incoherent, contradictory and unrealistic.

Yet for all the boos they elicit from experts, they draw frequent cheers at his rallies.

Scholars of American politics say this is because Mr. Trump, the Republican presidential nominee, is using international issues as a medium to connect with voters’ gut-level fears and desires, an approach that works precisely because his foreign agenda falls far outside the mainstream.

As Mr. Trump and his Democratic opponent, Hillary Clinton, meet on Wednesday for their final debate, in which foreign policy is slated to be a main topic, a look at his wholesale reframing of this set of issues reveals much about Mr. Trump’s improbable rise.

Studies show that most voters rank foreign issues low on their list of concerns, but they do listen and use those issues as a window through which they judge candidates’ values and ideology.