。
She lived her whole life as a single woman.
Literal
She [topic-は] lifetime single [as-で] persisted.
一生独身で通す is a fixed phrase combining 一生 ('lifetime / one's whole life') + 独身 ('single, unmarried') + で (means/manner) + 通す ('persist through, do all the way'). The verb 通す here means 'to maintain a stance / way of life through to the end' — same 通す seen in 信念を通す ('stick to one's convictions'). The で marks the manner: 'as a single person.' This is a slightly literary phrasing, often used for biographies or memorials of women who chose not to marry — a notable choice in mid-20th-century Japan, when marriage was the strong social default for women.