痛不欲生 is a four-character idiom formed by sequentially combining 痛 (pain), 不 (not), 欲 (want), and 生 (life). The characters construct a literal clause where 痛 indicates intense suffering, leading to the negation 不 of the desire 欲 for life 生, thus conveying the meaning of being in such extreme pain that one does not wish to live.