This is the 3632nd most frequent Portuguese word.
separados
"Separados" means "separated" in English.
Here 'separados' acts as an adjective describing the state of the papers being sorted into various piles.
Os papéis estão separados em diferentes pilhas.
The papers are separated into different stacks.
In this sentence, 'separados' describes the state of how they live, emphasizing their decision to remain apart.
Eles decidiram viver separados após o término do relacionamento.
They decided to live apart after the end of the relationship.
Here 'separados' is used in the passive form of the verb, indicating the action of sorting items to prepare them for delivery.