The newspaper industry is in a state of flux and has been for a long time now which is why I no longer work for one when they "outsourced" my entire department fifteen years ago. ALL communication media is in a state of flux whether it's print or digital and regardless of form theft has been and continues to be an ongoing problem whether people are stealing newspapers, movies, or music.
A certain amount of theft can be tolerated because the cost of eliminating it is more than it is worth. But when it goes past a certain line it really begins to hurt a business so it has to be stopped or the business go under.
People stealing out of newspaper machines is nothing new. It was a major concern when I was still in the business. People stealing all of the papers out of the box or stealing the paper box itself. It's simply theft and needs to be prosecuted.
Advertising does pay for the newspaper in large part. Just the paper. Not the necessary services that bring it to you. If you're not picking it up from the press building where it was printed then someone had to load that paper up and deliver it either directly to your home, a newspaper box, or a newsstand and that someone has to buy those papers first before they can bring them to you. When you put your money in the machine or you pay your subscription bill you are paying the person who makes the delivery. The newspaper company may handle the money, but they are doing it for the people who haul the newspapers and if those papers get stolen it's the folks who do that hauling that lose out. NOT the newspaper. Hauling papers pays poorly and it's a job that one has to be done seven days a week every week the year around and at very early hours of the day (if it's a morning paper) in order for you to get it when you want it.
It may be that one day the news printed on paper will go away in favor of an entirely digital media. Certainly enough newspapers have disappeared already. But that won't really change anything. Thieves will still find a way to steal from you. Wait... they already have, haven't they?