The elderly woman had been living alone in a three-bedroom apartment.

Literal

Elderly-woman [topic-は] 3LDK [possessive-の] apartment-complex [in-に] alone [by-で] was-living.

3LDK is a Japanese real-estate abbreviation: 3 rooms + Living + Dining + Kitchen. 集合住宅 (しゅうごうじゅうたく) is the formal term for apartment buildings. 独りで ('alone') adds pathos to a spacious apartment occupied by one person.