~そうになる (come to feel about to)

The pattern ~そうになる, combining the imminence/appearance ~そう (verb stem + そう) with なる ('become') to mean 'come close to / nearly X / start to feel about to X / be on the verge of X-ing.' Captures a near-event that almost happened: 泣きそうになる ('feel about to cry'), 眠りそうになる ('feel about to fall asleep').