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She fell asleep with her sweater still on.
Literal
She [topic-は] sweater [object-を] wore [still-まま] fell-deeply-asleep.
~たまま is the structure for 'in the unchanged state of having done X' — a past-tense verb pinned in place by まま ('as is, unchanged'). Common examples: 靴を履いたまま ('with shoes still on'), 電気をつけたまま ('with the lights left on'), 立ったまま ('still standing'). The subject did the first action and then a second event happened without resetting the state. 眠りこむ is a compound of 眠る ('sleep') + ~込む ('into / deeply') — meaning 'to fall deeply / heavily asleep', usually unintentionally.