So she's probably not hiding out.
The standing with her eyes closed sounds like maybe not feeling well.
Have you checked her over for injury or swollen belly?
Is she pooping OK?
This is what I do if I think a bird is ill:
I'd isolate bird in a wire cage within the coop for a day or two....so you can closely monitor her intake of food and water, crop function(checking at night and in morning before providing more feed), and her poops. Feel her abdomen for squishy or hard
swelling.
Best to put crate right in coop or run so bird is still 'with' the flock.
I like to use a
fold-able wire dog crate (24"L x 18"W x 21"H) with smaller mesh(1x2) on bottom of crate under tray.
Then you can put tray
underneath crate to better observe droppings without it being stepped in. If smaller mesh is carefully installed, tray can still be used inside crate.
Have you checked her over real well for mites and/or lice?
Best done well after dark with a strong flashlight/headlight, easier to 'catch' bird and also to check for the mites that live in structure and only come out at night to feed off roosting birds.
Google images of lice/mites and their eggs before the inspection so you'll know what you're looking for.
Wipe a white paper towel along the underside of roost to look for red smears(smashed well fed mites).
Part the feathers
right down to the skin around vent, head/neck and under wings.
Broodies flatten out on the nest and stay there for most the day and all night.
When you pull them out of nest and put them on the ground they will drop right back down flat on the ground like their legs can't hold them up.
They do not poop in nest but get up and out and drop the hugest smelliest poops ever.
They are often in a trance, but can hiss and spit and growl and bite if you disturb them,
but laying hens can do that too.
When they do get up too eat/drink/poop/dust bath, they will walk around clucking a soft low repetitive 'brood cluck'.
