Friends and relatives crowd into Su Zhen Chen’s small apartment in an East Village housing project, bearing food and solace for her and her husband. A community leader sometimes shows up to pay respects, or a military official arrives with papers to sign. Adults gather in the cramped living room for hushed chats in Chinese as children do homework at the kitchen table. For Ms. Chen, these are welcome distractions.

But at night, when the apartment goes quiet, the grief surges back, and Ms. Chen sits with a portrait of her son, her only child, and ponders what unfolded on a dusty military base half a world away. “It’s so sad that he loved the Army and this happened,” she said.

On Oct. 3, her son, Pvt. Danny Chen, was found shot to death in a guard tower on an American outpost in Afghanistan. He was 19 years old.

Three days after his death, a military official told Ms. Chen and her husband, Yan Tao Chen, that investigators had not yet determined whether the shot to the head was self-inflicted or fired by someone else.