。
She found a man lying dead.
Literal
She [topic-は] man [subject-が] is-dead [nominalizer-の][object-を] found.
Two structural points. The embedded clause 男が死んでいる ('a man is dead') takes its own subject marker が — inside subordinate clauses, the subject takes が, even when the sentence's overall topic is marked with は. The clause is then nominalized with の and made the object of 見つけた with を, giving the 'found-that-X-was-Y' construction. 死んでいる is the resultative ~ている, marking the persistent state resulting from the change-of-state verb 死ぬ ('die'); a literal 'is dying' reading would be wrong — it always means 'is dead.'