。
She was on the verge of fainting.
Literal
She [topic-は] fainting verge-of was.
気絶 ('fainting, losing consciousness') is yet another 気-compound: 気 ('spirit, consciousness') + 絶 ('cut off, sever'). 寸前 ('on the verge of, just before') is the productive suffix for 'right before X happens' — 出発寸前 ('right before departure'), 試合寸前 ('moments before the match'), 完成寸前 ('almost finished'). The structure is just noun + 寸前 + copula — no verb required. The whole sentence sketches a moment of crisis without saying she actually fainted.