One of my hens went missing for over 24 hours, so I sadly assumed she had been attacked by a predator, but today she ran back into the yard while I was outside. I noticed over the next several minutes that she did a large liquid poop and squatted a few times without expelling anything. I began to get concerned that she may be egg-bound. I finally caught her and was surpised that she is missing feathers on her abdomen.
Whereabouts are the missing feathers? If it's around the vent, it's not broody patches, but if it's her breast to belly areas, then it's most likely broody hormones causing feather loss in preparation for incubating eggs.
I felt her body and she seems thin, but could feel no eggs, except for what feels like a broken, empty egg high up on her chest.
You can't feel eggs in their chests. The lower body is where the eggs are formed. I think maybe what you're feeling is her crop. (?) If so, and if it feels 'broken' maybe she's swallowed non-edibles and they are impacted or just preventing her from digesting normally which would explain the weight loss. It can also slow down their whole digestive system until they are constipated and struggle to poop. But egg binding is still a possibility so don't rule that out.
This would explain the two or three eggs I have found in the nest box lately with what appeared to be yolk on them.
I would think the eggs with egg yolk on them are the work of something eating some of the eggs, possibly the hens themselves, or even just one of them.
So, it would seem that she is passing eggs, but there is that broken one inside. Is that possible?
Generally speaking, no, however I did hear recently of one hen who had internal laying issues for ages who passed a large mass of broken and combined eggshells. But she wasn't laying normal eggs during that time. They aren't capable of laying additional eggs when still egg bound with one.
I have her in a carrier and I am about to go buy some antibiotics and liquid calcium. Do I need to do a warm soak even though there don't seem to be any other eggs?
I'd use some lubricant both through her mouth and into the vent, like cold pressed olive oil, to see if that shifts her problems. But depending on what you feel in her crop, she may need the contents manually removed, either massaged up and out through her mouth or cut out. Crop surgery isn't the big deal it may seem, they tend to recover fine even if the crop has been totally removed. Due to fox attacks I ended up with several cropless chickens who nevertheless went on to heal and live normal lives.
Best wishes.