One of the characteristics of a self-organizing process, or spontaneous order, is the presence of power law distributions. In the market economy, for example, we see power law distributions of firm size and longevity.
Given that language is a spontaneous order, we should expect to see power law distributions of words. And we do. We see power law distributions of word use frequency, for example. But what about longevity? I don't know that anybody has specifically focused on this issue, but the recent discovery of word continuity that goes back as far as 15,000 years for the Eurasian languages, as discussed here, here, and here, is highly suggestive that we should be able to find a power law distribution or word stability across time as well.