The Catholic leader of the moderate Social Democratic and Labour Party, Hume was seen as the principal architect of Northern Ireland's 1998 peace agreement.
Britain and the EU have pledged to keep the border open after Brexit, but they have struggled to find a solution that is acceptable to both sides.
A former British soldier is set to be prosecuted in connection with the deaths of two civil rights protesters in Northern Ireland 47 years ago, part of an incident known as Bloody Sunday.
A vote to leave the EU would destabilize the 28-nation trading bloc, created from the ashes of World War II to keep the peace in Europe. A "remain" vote would nonetheless leave Britain divided and the EU scrambling to reform.