expression, ichidan verb
remain faithful to one's late husband; never remarry
Traditional phrase describing a widow who chooses not to remarry and stays devoted to her deceased husband's memory. Often carries a somewhat old-fashioned or literary tone.
祖母は若くして夫を亡くしたが、後家を立てて一生を終えた。
My grandmother lost her husband young, but she remained faithful to his memory and never remarried.
後家 is the noun meaning 'widow', while 後家を立てる is the verb phrase meaning 'to remain a faithful widow'.
The phrase combines 後家 (widow) with 立てる (to set up, establish), literally 'to establish oneself as a widow', implying a deliberate choice to remain unmarried.