This sounds like a headline and headlines often aren't proper sentences - they drop words for brevity and for added punch. If this headline was written properly, with the missing articles included, there is no ambiguity at all (although the word order could perhaps be improved):
A policeman shot dead an Apple area manager for not stopping his car.
(Taking this sentence in isolation and with the articles added in, it also now seems better not to use the narrative present, i.e. shot not shoots, but that has no bearing on any ambiguity either way.)
Your problem here is not with punctuation or the lack of it, nor with the English language per se, but with news headline-writing conventions. The abbreviated nature of headlines makes for more potential ambiguity, which is something bored subeditors sometimes abuse as a creative outlet... not in your example, though - I'm fairly certain the ambiguity is not deliberate as the joke just isn't that funny. (Sorry.)
I can't vouch for their veracity but some examples of headlines open to different interpretations follow - perhaps playfully ambiguous or perhaps accidentally ambiguous. The source claims they are "real newspaper headlines - gathered from local, national, and international newspapers across the globe." Whether deliberate, accidental, genuine or fake, they do serve to illustrate the point.
"Eye Drops Off Shelf"
"Prostitutes Appeal to Pope"
"Stolen Painting Found
"Queen Mary Having Bottom Scraped"
"Miners Refuse to Work After
Some of the general rules of headlinese follow:
Headlinese is an abbreviated form of news writing style used in newspaper headlines. Because space is limited, headlines are written in a compressed telegraphic style, using special syntactic conventions, including:
Forms of the verb "to be" and articles (a, an, the) are usually omitted.
Most verbs are in the simple present tense, e.g. "Governor signs bill", while the future is expressed by an infinitive, with to followed by a verb, as in "Governor to sign bill".
In the United States, conjunctions are often replaced by a comma, as in "Bush, Blair laugh off microphone mishap".
Individuals are usually specified by surname only, with no honorifics.
Organizations and institutions are often indicated by metonymy: "Wall Street" for "the financial industry", "Whitehall" for the UK government administration, "Madrid" for "the government of Spain", "Davos" for "World Economic Forum", and so on.
Many abbreviations, including contractions and acronyms, are used: in the US, some examples are Dems (for "Democrats") and GOP (for the Republican Party from the nickname "Grand Old Party"); in the UK, Lib Dems (for the Liberal Democrats), Tories (for the Conservative Party). The period (full point) is usually omitted from these abbreviations, though U.S. may retain them, especially in all-caps headlines to avoid confusion with the word us.
Lack of a terminating full stop (period) even if the headline forms a complete sentence.