I just heard a radio news report on a murder: "The victim was found by a passer-by with stab wounds".
Surely this should read: "The victim, with stab wounds, was found by a passer-by"?
The context makes it clear who had stab wounds. I don't see anything wrong with the headline, or with your alternative. Both are ok.
Alternatively, it could say:
Passer-by finds victim with stab wounds.
The headline is ambiguous, but not as has been described so far. The passer-by could have stab wounds (restrictive prepositional phrase), or the finding could have been done with stab wounds (adverbial prepositional phrase). The intended meaning (that the victim had stab wounds) is NOT being stated. It is only our assumptions that lead us to that conclusion. How would you parse this headline: "Dog bites man with rabies"?
Lately, I've started to eschew putting adjectives at the end of sentences like this, precisely because of you ambiguity you mention in this example. In this particular case, I agree with the other poster that the description of one person as "the victim" implies that he/she is the one with the stab wounds in this case, but there are many other cases where the nouns do not remove the ambiguity.
I think your suggestion of "The victim, with stab wounds, was found by a passer-by" is an improvement, but the positioning of your adjectival phrase makes it sound like you're clarifying which victim (eg. "The victim with stab wounds was found by a passer-by, while the victim with head trauma was found by a rescue dog" - now, I removed some commas in my example, which changes the meaning more toward the point I'm trying to make, but you get the idea).
Actually, I feel it's best re-worded at "The victim was found, with stab wounds, by a passer-by". Here, we're clarifying something about how they were found... suggesting that this was a condition specific to that moment.
I would view the statement "The victim was found by a passer-by with stab wounds" as an error, assuming, of course, that it's the victim that has the stab wounds. "With stab wounds" refers to the passer-by; we know that's illogical, so we know what the writer is trying to say. But what he's trying to say isn't what he said.
The New Yorker made fun a few years ago of a statement about "A table purchased by a lady with Heppelwhite legs." We may know what is meant, but to attach the prepositional phrase to "a lady" is simply an error.
@Ami's sentence "Dog bites man with rabies" clearly implies that the man has rabies.
"The car was parked by a woman with the motor running." Surely that's an error.