I found four injured men alive.
In this sentence, the adjective "alive" comes after the noun "men".
Why we have to use adjective "alive" after the noun, not before? because in adjective order, adjectives should come before the nouns.
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It's a stylized use of "find". You can "find [something] to be [some adjective]". The "to be" is optional.
I found her (to be) perfectly charming
I found the dinner (to be) almost inedible.
I found the movie (to be) exciting but implausible.
In a similar way, in your example sentence, the writer found the injured men to be alive.