Because it is kept very cold and at a specific humidity. Beef can be aged at 1-2°C, which keeps a lot of spoilage at bay, and the dry environment does the rest. Dry and cold = slower decay.
That said, some stuff *does* happen. The beef breaks down. A very simple way to think about it is that it decays, but without any nasty bacteria or fungus. Enzymes start to break down the meat. Chemical changes happen. That is what makes dry aged beef so tender and flavorful.
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