What is happening is that your bird was eggbound and the egg continued to have layer after layer added. I suspect it was also cooked by her body temperature.
The most important thing for you do to immediately is take stock of your feeding program.
Laying hens should always have 90% or more of their diet as a completely fortified laying feed. The other 10% can be more of the same, or treats, or grains.
The reason is that laying pellets are designed with the right ingredients to allow calcium absorbtion and utilization. Calcium absorbtion is a three-legged stool, the three legs being calcium, vitamin D, and phosphorus.
If any of the legs are too much or too short, the whole stool falls. The poultry industry has put years and years of research into what a hen needs to lay good solid eggs. Take advantage of it.
You should also be providing free-choice oyster shell always to laying hens. Laying feeds are designed after years of research for a scientifically average hen who needs approximately .45% of her daily intake as calcium with a ration of at least 6 parts calcium to 1 part phosphorus.
However some perfectly healthy hens can need as much as 15 parts calcium to 1 part phosphorus! The feed manufacturers can't provide a 15:1 ratio in feeds because it would be toxic to force the 6:1 needing hens to have that much calcium. They assume that the savvy poultry man will provide either oyster shell (or in the old days, lime grit). Oyster shell is a highly bioavailable source of calcium as it dissolves readily when in the gizzard being ground down. Unlike egg shells fed back, it readily absorbs into the blood stream. Hens who need more calcium have an instinct for picking up oyster shell if you show them it's there.
Phosphorus is rarely deficient as it's provided by cereal grains of which feed is mostly composed. If anything, too often phosphorus is too high in the diet as people supplement with a good deal of grains. If the body gets in too much phosphorus, it will take calcium from the egg-making process to handle and bind with the phosphorus. If the grain overage continues, the hens can actually deplete their very bones to make up for too much phosphorus, resulting in adult rickets. More often, we see soft shelled eggs, followed by "no egg" which are more often shell-less eggs that never leave the body. So keeping grain levels in control is vital.
Vitamin D is sometimes deficient. For your hens, I would recommend a 2 week regimine of some cod liver oil on top of their feed - very little, say cod liver oil sprayed on top of the feed twice weekly from a hand-held mini sprayer like you use for gardens or found in the cosmetic section. That provides enough vitamin D without overdosing. (More is not necessarily better in this case.)
For this hen, I would definitely recommend a one-time serving of a 1/2 tums tablet crushed into a treat or served on watermelon for example. The other hens wouldn't hurt to have it as well, but this one is having what I call "sticky" eggs - eggs that are likely not quite hard enough that as a result aren't sliding through the cloaca.
I feel that if you follow my advice, you might be surprised at how your hens turn around.
