。
She remembered her first love until the day she died.
Literal
She [topic-は] death [until-まで] first-love of thing [object-を] forget-not was.
忘れずにいる ('not forgetting, keep remembering,' literally 'be in a state of not forgetting') uses ~ずに ('without doing') with いる ('to be'). The construction expresses a state of continuous non-forgetting — more poetic than 覚えている ('remember'). 初恋 ('first love') is a culturally weighted word in Japan, with its own genre of literature, songs, and 思い出話 ('reminiscing'). The pairing of まで死ぬ with the precious-memory image makes this sentence quietly powerful.