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She had the handbag she bought last week stolen from her.
Literal
She [topic-は] last-week bought handbag [object-を] was-snatched.
先週買った modifies ハンドバッグ as a relative clause — 'the handbag she bought last week.' The passive 奪われた (from 奪う, to snatch/steal) puts her as the victim. This is a direct passive: she was robbed of something she possessed. The recent purchase (先週買った) adds emotional weight — something newly acquired was immediately taken. ハンドバッグ is a loanword from English 'handbag.'