I have a hen that is a little over a year old. She recently has been having some troubles with laying eggs that have thin shells/no shells.
That's challenging. I assume her egg shells were fine until recently. How long is recently and how consistent is it? Are your other hen's egg shells OK? When I have an issue I try to determine if it is an individual issue or a flock-wide issue. I don't want to mess up the rest of the flock by treating them when nothing is wrong with them.
How long has she been laying without stop. Sometimes egg quality can deteriorate late in a hen's laying cycle. That's one reason they need to molt and recharge their system. Each hen is an individual and some are affected by this more than others. Usually it takes 13 months or more for this to start showing up but you never know.
Some hen's bodies don't absorb certain nutrients the way they should. They just don't process them right, no matter how much they eat. Often it is genetic. If her egg shells used to be fine this is probably not it. Then there is Vitamin D.
Most hens know by instinct that they need extra calcium for egg shells and will eat enough oyster shell or other calcium supplements if they need them. But not all of them have the right instincts.
Is it every egg she lays? Hens typically only make a certain amount of shell material per day. It is possible for a hen to release more than one yolk per day to start the internal egg making process. When that happens there may not be enough shell material to go around so the later eggs especially can be thin-shelled or even soft-shelled. Double yolked eggs can sometimes be thin.
I'll mention this one but I don't think it is what is happening to you. When a pullet starts laying the eggs are pretty small. If she is making enough egg shell material those shells can be pretty thick. As the eggs get larger the shell material has more egg to cover so the shells get thinner. I find it highly unlikely the eggs have increased that much in size lately.
Are they getting a period of dark time? They need enough dark to rest and regroup at night. That can lead to egg quality problems but usually not something like this.
This is what the Egg Quality Handbook has to say about it. This is more for commercial egg production but some of it carries over to our backyard flocks.
https://thepoultrysite.com/publications/egg-quality-handbook/16/thinshelled-eggs-and-shellless-eggs
I'm having problems coming up with things I think it could really be as I understand that this is a recent change. Maybe you can see something in all this that gives you a clue.