European Union officials were working frantically. Top brass from across the continent had flown to Washington to meet with President Trump about the future of the war in Ukraine, and officials were scrambling to relay news and to work on a plan for peace.

Emails zinged. Phones buzzed. Videoconferences overlapped.

But at the E.U. headquarters in Brussels last week, silence reigned.

A lone security guard leaned against the European Commission’s Berlaymont building and tapped his foot, visibly bored as he manned the visitor’s entrance. There were few journalists and other guests to screen. The wide sidewalks of Brussels’ government district, usually thronged with diplomats and politicians, were bathed in balmy sunshine and nearly empty.

“On a normal day, this building is full of people,” said Wopke Hoekstra, the European commissioner for climate and one of the few E.U. officials in the building last Tuesday.

Mr. Hoekstra was the E.U.’s “designated survivor” for the week. Diplomats and journalists in Brussels use the title as a tongue-in-cheek nod to the American practice of holding a potential presidential successor back from big events to ensure that the entire government cannot be taken down at once.