From The Washington Post:

The vast majority of Department of Homeland Security employees would continue to work under a government shutdown because their functions “must be maintained under all circumstances to ensure the safety and security of the nation and its citizens,” or because their jobs are not funded by congressional appropriations, according to the agency’s 2013 contingency plan. The DHS plan designates about 86 percent of the department’s roughly 231,000 employees as “essential,” meaning they would remain on the job for the “safety of human life or protection of property.”