Hens only lay an egg a day. So it takes a week to lay a typical clutch of 6 eggs. However they don’t want to still be sitting on eggs when they have week old chicks to feed. They want all their chicks to hatch within a couple of hours of each other. To achieve that they’ve evolved a system whereby the eggs survive when incubated at normal body temperature, but they don’t develop. They only start to develop when incubated at higher than normal body temperature.
So a clucky hen retains her normal body temperature for the first week or so, and any eggs laid at that time will not start to develop. Then her body temperature increases and all the eggs start to develop at exactly the same time.
So long as you collect your eggs at least once a week there is no chance the embryo will have started to develop.
I assume the animal would have been skinned (leather was also a valuable resource on the frontier remember) and presumably gutted as well. So I’m imagining the cleaned carcass including head and feet would have gone into the pot.
And yeah, any rendered carcasse stinks, but as t-bonham notes, it was done in an outdoor kitchen, or more commonly in a kettle or, in later days just an old drum, over an open fire. This wasn’t fine cuisine. The idea was to boil the carcasse down into tiny bits that the hens could easily eat. So long as it was literally boiled to bits it was acceptable.
However, it’s easy to miss eggs, and you can miss a hen incubating if you have a lot of chickens. I grew up eating eggs from farms where roosters were kept with the hens, and I have crunched down on little embroyos a couple times.
I haven’t had this issue yet with my current pastured egg provider, and I know they also keep roosters with the hens (when chickens are truly free-range roosters are pretty valuable for protection).
I’ve seen some Food Channel show probably with Andrew Zimmern at a food stall in Asia. One of the specialties was pre-laid eggs which were pretty much just yolks of various sizes. I seem to recall there were about 4 of them. I’m sure there were more, but they were probably too small to be worth eating.
