I would definitely think about culling her. I have about 33 laying hens (not including 20+ young pullets) and I have one hen that I cannot identify that lays a very soft shelled egg about 3 times a week. They never make it out of the nest box before being broken (and eaten by somebody). It's just a big, nasty mess to clean up. They all get adequate amounts of protein and calcium, are free ranged half the day and get scraps from us. I don't think it's nutritional. I suspect something's not right internally and it will end up being an internal laying scenario.
Any ideas how I can identify the culprit?