Learn Portuguese (Portugal): Desabado o teto, eles procuraram os feridos nos escombros. - After the roof collapsed, they searched for the injured in the rubble.

This is an Absolute Participle Clause. It uses the past participle (desabado) to express an action that was completely finished before the main part of the sentence happened. It translates to "The roof having collapsed" or "Once the roof collapsed" and is a more elegant, concise alternative to saying Depois de o teto desabar.

Why does the participle come before the subject in "Desabado o teto"?

In Portuguese Absolute Participle Clauses, the standard word order is to put the participle before the noun it refers to. Saying O teto desabado at the start of the sentence would sound more like a descriptive subject ("The collapsed roof") rather than a completed background action ("Once the roof collapsed").

Does the participle "desabado" need to agree with "o teto"?

Yes. In these clauses, the past participle behaves like an adjective and must match the gender and number of the noun that follows it. Because o teto is masculine singular, we use desabado. If the walls had collapsed, you would say Desabadas as paredes, matching the feminine plural noun.

Is "feridos" acting as a noun or an adjective in this sentence?

It is a past participle acting as a noun. Just like in English ("the injured"), Portuguese allows you to place a definite article (os) directly in front of an adjective or participle to refer to a specific group of people characterized by that word.