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Hi I'm Dr. Bonk. I'm sorry to hear about your chicken's troubles. Soft shelled eggs are usually the result of a calcium or vitamin D deficiency. Calcium is the main component of egg shells so chickens require a lot of dietary calcium when laying. Vitamin D is also important for calcium absorption. If you are not currently providing a calcium supplement, it would be time to add one. One of the most common is oyster shell. You can also add good quality alfalfa or clover as a calcium source. If you have any eggs with normal shells, you can feed them those crushed up as well. In some cases, you may need to add liquid calcium to the water.
Make sure your hens have access to the outside sunshine to produce vitamin D. A couple hours a day is enough for most hens.
Finally, hens can lay soft shelled eggs during molting. This is just due to the extra stress on their bodies. Since your hens are losing their feathers right now, they could be molting. Usually hens don't lay during this time or their production drops. This is a very stressful time and they may need extra supplements of protein and calcium to help get them through it. You can supplement protein by feeding canned meats or fish or by cooking eggs for them.
Make sure their main food source is a good quality one and that they have lots of fresh water. Also make sure there are no other stressers in their environment such as barking dogs, heat, cold, etc.
I hope this helps. Please contact me with any further questions you may have. Thank you and good luck!