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Decades of research in ecology have shown that nestedness is a ubiquitous characteristic of both, biological and economic ecosystems. The dynamics of nestedness, however, have rarely been observed. Here we show that the nestedness of both, the network connecting countries to the products that they export and the network connecting municipalities to the industries that are present in them, remains constant over time. Moreover, we find that the conservation of nestedness is sustained by both, a bias for industries that deviate from the networks' nestedness to disappear, and a bias for the industries that are missing according to nestedness to appear. This makes the appearance and disappearance of individual industries in each location predictable. The conservation of nestedness in industrial ecosystems, and the predictability implied by it, demonstrates the importance of industrial ecosystems in the long term survival of economic activities.