to die; to stop breathing — to lose one's life (somewhat literary).
老犬が静かに息絶えた。
The old dog quietly passed away.
彼は現場で間もなく息絶えたと報告された。
It was reported that he soon died at the scene.
夜中に祖母の呼吸が弱くなり、やがて息絶えた。
My grandmother's breathing weakened during the night, and then she passed away.