Примеры

он было стал засыпать - he had nearly fallen asleep, he was on the point of falling asleep, he was just going to fall asleep
он было не хотел приезжать - he was on the point of not coming at all; he very nearly didn't come at all
чуть было не - (very) nearly; on the point of
он чуть было не забыл - he very nearly forgot
его чуть было не убило - he was nearly killed
он чуть было не ушёл - he was just about to leave, he was on the point of going