Sure they can. There are a couple reasons why. First, even though it is "private property", it is still open to the general public. Second, the stop sign may be a requirement per city or state code. The same code may give the local police jurisdiction for traffic control in the parking lot. Traffic laws don't end at the edge of the property line.
Can a police officer pull me over for failing to stop at such a sign when it does not occur on public/state/government property? Or can they pull me over and site me for "failure to stop" at a stop sign?
If you feel my answer is rude, mean, snarky or in anyway not to your liking, I did my job. You don't need to tell me.
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