She remained single her entire life.

Literal

She [topic-は] lifetime single was.

生涯 (しょうがい) means 'one's entire life' or 'lifetime.' 独身 (どくしん) means 'single/unmarried.' であった is the formal past copula — more literary than だった. The sentence has a quiet, biographical finality to it: her marital status is stated as a lifelong fact.