Because I just can't help myself I was reading about self-organized criticality the other day, That subject is not particularly precisely defined, but there's a nexus of models in which events emergently take place on different scales with a frequency that obeys some power law with respect to the scale. People certainly find power laws in economics, and I've thought of reasons an economic system might be naturally driven toward critical points, but aside from a brief and particularly fuzzy attempt 25 years ago, there hasn't been much SOC in the economics literature.
I also, you may have noted, have an abiding interest in "liquidity", in its various guises. One of the key characteristics of liquidity is its heterogeneity; "liquidity shocks", for example, can be idiosyncratic or systemic — or, possibly, somewhere in between. If I suffer an idiosyncratic liquidity shock, I can sell some assets to other people to raise cash for my sudden needs. If everyone suffers a liquidity shock at the same time, then nobody else particularly wants to buy; at best, I'm selling at much lower prices to people whose sudden liquidity needs aren't quite as dire as mine. I haven't seen literature that mentions in-between events, but it would seem reasonable to me that both the contagion effects of liquidity shocks and the triggers of liquidity shocks would have some of the local-interactions-with-threshold-effects characteristics that SOC models tend to have, and would exhibit some of the power law behavior that tends to result.