。
Her son was her one and only reason for living.
Literal
She [topic-は] son [only-だけ] [subject-が] reason-for-living was.
生きがい ('reason for living, purpose in life, raison d'être') is one of the celebrated 'untranslatable' Japanese words — popularized internationally in the last decade. Built from 生きる ('live') + 甲斐 ('worth, value, effect'). Captures the personal anchor that makes life feel worthwhile. The combination ~だけが生きがい ('X is one's only reason for living') is a familiar phrasing — often somber, expressing emotional dependence on a single source of meaning. ここに pattern: 息子だけ (only the son) + が as identificational subject of 生きがい.