。
She had been sitting slumped on the sofa.
Literal
She [topic-は] sofa [genitive-の] top [on-に] sloppily hips [object-を] was-lowering.
腰を下ろす ('lower one's hips') is a slightly more deliberate phrasing for 'sit down' than the everyday 座る — it draws attention to the physical act of taking a seat. だらしなく ('sloppily, in an unkempt way') is the adverbial form of だらしない, an adjective applied to anything from posture to morals to dress sense; here it conjures someone sprawled rather than seated. ソファー is one of a long parade of household-furniture loanwords (テーブル, カーテン, ベッド, タンス) that have largely displaced any native equivalents in modern speech.