Usually this random egg-appearing-in-the-run thing is associated with new layers not quite yet having the nest box habit. But I've had a lazy Welsummer well into her mature years do it.
I am grateful when I find such an egg unmolested, but I really have never been able to identify my shiftless little layer.
One other possibility is an egg is laid in the nest box but due to very fine butt feathers and an exceptionally wet, sticky egg, the hen then "wears" the egg out of the coop which eventually works its way loose and drops in the run. I got this photo of the egg stuck to my Cochin's butt feathers after solving the mystery of why so many tan eggs were ending up in the run.
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