絶える
たえる · taeru · JLPT N1 · verb-ichidan
to die out
🦤 絶 (zetsu) = cut off, sever; 絶える = a line cut off until it dies out
The kanji 絶 means cut off or sever, as in 絶縁 (insulation, cutting a connection). When a species or family line is cut off from continuing, it dies out.