on the verge of starvation; at the point of starving
Describes a critical state of extreme hunger, often used figuratively for dire need.
They were on the verge of starvation and needed food immediately.
Compound of 飢餓 (kiga, 'starvation') + 線上 (senjō, 'on the line') + に (ni, adverbial particle), literally 'on the starvation line'. The exact historical derivation is uncertain, but the phrase is conventionally associated with the brink of starvation.