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She pretended to be sick as an excuse.
Literal
She [topic-は] excuse [as-として] sickness [of-の] pretense [object-を] did.
Two patterns in tight sequence. ~として ('as, in the role of') frames 言い訳 ('excuse') as the function of what comes next — 'in the capacity of an excuse.' Then 病気の振りをする ('pretend to be sick') uses the idiom 振りをする ('do a pretense'), with の attaching the thing being feigned. The pattern is fully productive: 知らない振りをする ('pretend not to know'), 寝た振りをする ('pretend to be asleep'). 仮病を使う ('use a fake illness') is a near-synonymous expression specifically for faking sickness — both are stock phrases in stories about skipped school days and missed obligations.