As Russian forces mount an offensive, Ukrainians in Kupiansk fear a second occupation.

Clockwise from top left: A destroyed bridge in Kupiansk, a Ukrainian soldier extinguishing a fire that started after shelling, a local prosecutor at a former police station that he said had been used as a torture center, Liudmila Sezonova and her son in their home.Credit…Emile Ducke for The New York Times

A billboard at the main entrance to the city of Kupiansk illustrates the tenuous nature of Ukrainian control in a region that has become one of the most active parts of the 750-mile front line in the war.

“Kupiansk is Ukraine!!!” it proclaims to anyone entering the city. The other side of the sign, visible to those in the city center, hints at why the first proclamation is so urgent. It shows an armed soldier standing in front of a helicopter, along with a phone number and a question: “Do you have information about traitors to Ukraine?”

At the outset of the war, Kupiansk, only 25 miles from the Russian border, fell to Moscow’s forces without a fight and remained under occupation for six months before being retaken in a lightning Ukrainian thrust in the Kharkiv region in the country’s northeast in September.

Now, however, while most attention is focused on the latest Ukrainian counteroffensive hundreds of miles to the south, Russian forces are mounting an offensive in the north, seeking to regain those lands. Kupiansk, a strategically important city that served as a logistical center for the Russian military, is right in the cross hairs, and many residents say they dread the return of the forces who terrorized them for six months.

“No one can survive a second occupation,” said Liudmila Sezonova, who runs a honey wholesale business and said she stayed home for months throughout the occupation, hoping that she would not be penalized by the Russians for being a Ukrainian patriot.