Poor and pregnant, the woman moved into Room 4 of the shelter in early May with her 9-year-old son. She had escaped her abusive husband. But now, the Russians were coming.

For vulnerable women near the front lines like Nina Holubieva, the women’s shelter in Sumy, Ukraine, near the Russian border, has become a last resort, a refuge from abusive men that also takes in vulnerable poor mothers. Yet even as they flee violence at home, the women are desperate to escape the encroaching war outside. As the Russians started pushing into the Sumy region this spring, that became much harder.

“I wanted a family, I wanted something decent,” said Ms. Holubieva, 37, who on a recent Saturday wore a donated shirt proclaiming “Victoria’s Secret Angel” and a tangle of dark hair pulled back in a ponytail. “But this is how it turned out.”

Russian troops first crossed this border in January, part of their effort to drive Ukrainian troops out of the neighboring Kursk region of Russia. Now, Russian soldiers are about 13 miles from Sumy, a city of about 256,000, even as Ukrainian officials say troops have stalled their advance.

Explosions shake the windows and doors of the shelter, the Mother and Child Center, almost every day. A nearby building no longer has a wall; from the street, you can see a pink-tiled bathroom on the top floor and a cracked hallway mirror, reflecting the gray sky.