。
She wept at her son's death.
Literal
She [topic-は] son [genitive-の] death [at-に] cried.
に here marks the cause/trigger of crying — Japanese consistently uses に for the stimulus of an emotional reaction. 息子の死に泣く ('cry at son's death'), 不幸に泣く ('cry at misfortune'). Compare で which would emphasize the source/origin (悲しみで泣く 'cry from grief'). The two are close but に focuses on the trigger event, で on the emotional cause.