She said she hadn't stolen anything.

Literal

She [topic-は] anything [also-も] didn't-steal [quotative-と] said.

何も + a negative is the standard 'nothing' construction — 何も alone has no fixed meaning; the negation completes it ('not anything' rather than 'nothing'). The reported clause sits inside the と + 言った frame as indirect speech, with no quotation marks needed: Japanese marks the boundary by structure, not punctuation. The bare past 言った keeps the sentence casual and narrative rather than a courtroom report.