。
She remembered the cat that had been left behind at home.
Literal
She [topic-は] home [at-に] been-left cat [of-のこと] [object-を] remembered.
Inside the noun-modifying clause 家に残された猫 ('the cat that had been left behind at home'), the verb is in passive form: 残された ('was left'). Passive in relative clauses is one of the standard ways Japanese builds 'X-ed N' phrases — equivalent to English '-ed' participial modifiers. The のこと softens the object slightly when the object is something/someone with personal connection: ~のこと(を)思い出す = 'remember (about) ~,' preserving the warmth of the connection rather than treating the cat as a bare grammatical patient.