The name says it all really. If someone wanted to collect insurance money on their car could they leave it somewhere with a high crime rate with keys in ignition and a sign that basically invites a theft of the car to collect the insurance? So long as they don't actively arrange for someone they know to do the theft would they be able to collect insurance on the car, even if the agency knew what they had done?
What you are describing may be the crime of insurance fraud: to avoid that, you would have to admit to the insurance company that you put a "Please steal me" sign in an unlocked car with the keys in the ignition, in a high-crime area. If we remove some of the elements of the scenario and reduce this to "leaving the keys in the ignition", this would probably be be considered contributory negligence, meaning that you failed to act prudently to protect your property. This can reduce the amount that the insurance company has to pay you. At this point, it depends on what state you're in, since sometimes a little bit of negligence (in Alabama, Maryland, North Carolina, and Virginia) means that you may get nothing. However, negligence hinges on an assessment of the actions and intentions of a party, and what you describe isn't "neglect", there is the direct intent that the car be stolen. Insurance policies exclude coverage for intentional loss.
So the bottom line would be that the person would be out a car, and could be in prison for fraud if they did not reveal what they actually did. One should assume that the thieves took a lulz video of the sign before they stole the car, and posted it on FaceTube where it entered the viral hall of fame and was used against you in a court of law, so fraud is the worst choice. An alternative if you have a car is to donate it to charity, and take a tax write-off.