Below are some info bits I found that sound like what you're describing. I'm sorry you lost your girl. :(
The first pullet egg may be soft-shelled until her system gets into its stride. If it continues, make sure that the birds are getting a balanced diet such as that provided by a commercial free-range or organic layer’s ration. Such feeds will usually contain calcium and phosphorus in the right ratio (around 3.5-4% calcium to 0.3% phosphorus). Providing a little crushed oyster-shell or calcified seaweed will ensure that any deficiency is rectified, for the birds will not take more than they require.
A shock can also make a hen lay a soft-shelled egg. My own observations are that if a flock is caught in a sudden shower of rain (for they are sometimes too dim to run for shelter), a few soft-shelled eggs are often produced the next day, but by the following day, they’re back to normal.
It is when soft-shelled eggs or misshapen ones are produced regularly that there need be a cause for concern. Veterinary advice should be sought. Conditions that adversely affect eggs include Newcastle disease (a notifiable disease to the authorities) and Infectious bronchitis, but there would be disease symptoms showing in the birds themselves if either of these was present. Hybrids are normally vaccinated against them.
Egg drop syndrome (EDS) is also a viral infection that results in a reduced number of eggs, as well as an increased number of pale-shelled eggs. Birds do recover from it but egg production may not get back to its previous level and there may still be a proportion of deformed ones produced. It can be vaccinated against.
These differ from middle-banded eggs in having a range of distortions, including soft ends and uneven or ribbed surfaces. Thin patches or excessively chalky areas may also be seen. They are more common with older hens, but may also indicate a disease such as Infectious bronchitis or egg drop syndrome (either present or past). If the condition persists, veterinary advice should be sought.
There are obviously quite a few things that can go wrong with eggs, but it is also worth pointing out that it is a minority of eggs and chickens that are affected by problems. If chickens are well-fed and housed, in clean conditions and with access to plenty of fresh air and good ranging space, they are likely to remain healthy and productive for a long time.
An occasional misshapen egg is no cause for concern, but a hen that typically lays odd-shaped eggs will pass the trait on to her progeny.
Bloody shells sometimes appear when pullets start laying before their bodies are ready, causing tissue to tear. Other reasons for blood on shells include excess protein in the lay ration and coccidiosis, a disease that causes intestinal bleeding. Cocci does not often infect mature birds, but if it does you'll likely find bloody droppings as well as bloody shells.
Chalky or glassy shells occasionally appear due to a malfunction of the hen's shell-making process. Such an egg is less porous than a normal egg and will not hatch, but is perfectly safe to eat.
Odd-shaped or wrinkled eggs may be laid if a hen has been handled roughly or if for some reason her ovary releases two yolks within a few hours of each other, causing them to move through the oviduct close together. The second egg will have a thin, wrinkled shell that's flat toward the pointed end. If it bumps against the first egg, the shell may crack and mend back together before the egg is laid, causing a wrinkle.
Weird-looking eggs may be laid by old hens or by maturing pullets that have been vaccinated for a respiratory disease. They may also result from a disease itself, such as infectious bronchitis. Occasional variations in shape, which can be seasonal, are normal. Since egg shape is inherited, expect to see family similarities. If you do your own hatching, select hatching eggs only of normal shape and size.
Thin shells may cover a pullet's first few eggs or the eggs of a hen that's getting on in age. In a pullet, thin shells occur because the pullet isn't yet fully geared up for egg production. In an old biddy, the same amount of shell material that once covered a small egg must now cover the larger egg laid by the older hen, stretching the shell into a thinner layer.
This flat-sided turkey egg appeared after the hen crash landed off the barn roof.
Shells are generally thicker and stronger in winter but thinner in warm weather, when hens pant. Panting cools a bird by evaporating body water, which in turn reduces carbon dioxide in the body, upsetting the bird's pH balance and causing a reduction in calcium mobilization. The result is eggs that are thin-shelled. Thin shells also may be due to a hereditary defect, imbalanced rations (too little calcium or too much phosphorus), or some disease—the most likely culprit being infectious bronchitis.
Soft or missing shells occur when a hen's shell-forming mechanism malfunctions or for some reason one of her eggs is rushed through and laid prematurely. Since the shell forms just before an egg is laid, stress induced by fright or excitement can cause a hen to expel an egg before the shell is finished. A nutritional deficiency, especially of vitamin D or calcium, can cause soft shells. A laying hen's calcium needs are increased by age and by warm weather (when hens eat less and therefore get less calcium from their rations). Appropriate nutritional supplements include free-choice limestone or ground oyster shell, and vitamin AD&E powder added to drinking water three times a week.
Soft shells that are laid when production peaks in spring, and the occasional soft or missing shell, are nothing to worry about. If they persist, however, they may be a sign of serious disease, especially infectious bronchitis, Newcastle disease or infectious laryngotracheitis, all of which are accompanied by a drop in production.
Broken shells often result when a thin or soft shell becomes damaged after the egg is laid. Even sound eggs may get broken in a nest that's so low to the ground the chickens are attracted to scratch or peck in them. Hens and cocks may deliberately break and eat eggs if they are bored or inadequately fed. Boredom may result from crowding or from rations that allow chickens to satisfy their nutritional needs too quickly, leaving them with nothing to do.
A chalky egg (right) occasionally appears as a quality control glitch in a hen's reproductive system.
If your coop is small and well lighted, discourage non-laying activity in nests by hanging curtains in front to darken them. To allay a hen's suspicions about entering a curtained nest, either cut each curtain into hanging strips or temporarily pin up one corner until the hens get used to the curtains.
Hens may break eggs inadvertently. Such accidents commonly occur if nests contain insufficient litter, eggs are collected infrequently enough to pile up in nests, or nests are so few that two or more hens crowd into the same nest at the same time. Sometimes timid birds seek refuge by hiding in nests, and their activities may break previously laid eggs.