She outlived her son.

Literal

She [topic-は] son [by-に] was-preceded-in-death.

先立たれる is the passive of 先立つ ('to predecease, go before in death'). The passive form gives the sentence its 'outlived' meaning from the surviving parent's perspective — 'was preceded [in death] by her son.' This is one of the canonical adversity-passive examples: the subject is the affected party (the parent), and に marks the deceased person (the son). The structure is a polite, slightly formal way of saying 'to lose a child' — a phrasing learners studying Japanese euphemism should know.