There can be a problem with a bird's calcium metabolism also. We had one hen that would lay doube-yolkers (once laid a triple yolker) but also laid very thin-shelled eggs and in later years we would find broken eggs or eggs with just the membrane and no shell. THis was despite us feeding dried and crushed eggshell back to the hens.
It's a good habit to get into, to dry your eggshells and feed them back to the hens.
What we do, is we have a small metal tray which we keep in the oven. When we use an egg, we put the shell on the oven tray. When the oven is in use we remove the tray but when we turn the oven OFF, we put the tray in the oven and residual heat dries the shells well. If you try to crush the shells before drying them out, they will form a gluey mess because egg-white takes a while to dry out and is like glue if it's at all moist.
We put the crushed shells into either the food hopper, or spread over the deep litter of the chookhouse floor. Our chooks have an earth floor covered with plastic netting (allows earthworms through but not digging foxes). We have four courses of loose-laid bricks and sitting on top of the brick wall is a timer frame wrapped in chicken wire. The cavity inside the brick wall is filled with straw or grass clippings, all vegetable scraps go here. We keep it as dry as possible, and it doesn't smell if it's left dry. It also keeps the chooks warm in winter. We have a fibreglass sheet roof over it all.
So if we choose to toss ground eggshells into the chookhouse on the floor, the chooks eat what they get to and anything else adds to the compost and helps 'sweeten' the soil, like adding garden lime. To get access to the best stuff for the garden, we can either dig it out from the top, or occasionally when the brick wall begins to collapse we knock out a few bricks, dig out from there (reduces the pressure, anyway) then re-build the brick wall hole to fill it back in until next time.
Back to the eggs and shells - yes, chooks do well if you give them extra calcium. Depending on what you're feeding them, they should be getting enough calcium in their diet but a bit more never hurtsd. Crushed oyster shell would be the same composition chemically - calcium carbonate. But why go out and get oyster shell if your chooks are providing you with their own calcium carbonate?
A normal egg is surrounded first by a thin leathery membrane (it is a semi-permeable membrane, like onion skin is) and then a layer of calcium carbonate is laid down over the top. If a chook has a faulty shell gland then they may not lay down the calcium carbonate layer, and you get this odd thing that feels like it's been wrapped in tough paper. The egg inside is perfectly usable as with any other egg, but they don't keep well because it is far more permeable and will go off much sooner (assuming you could leave it that long). Don't try to boil it, but you could open it and poach or fry it. Or use it in any other conventional way. My dad used to feed those ones to the dogs, because it saved him the trouble of carrying them up to the house and then having to find a way to store them safely without them getting so easily broken.
If the other hens are laying eggs with good, firm shells, then you could hae a hen with a problem. Keep an eye on what she lays, keep feeding shells back to them but if you're not getting anything useful from her, you may need to "reconsider her role in the flock" - a euphemism for Sunday chicken roast.
Or do what we did - keep her on as a pet. Not sound farming practice, but it keeps the kids happy.
Marg