Answer: I have not grown this particular summer squash, but I can speculate on what's going on here. The swollen area behind the female flower is the ovary; once the flower is pollinated and the egg is fertilized, the ovary is technically called a fruit. It sounds like, in this variety, the ovary enlarges quite a bit before the flower is pollinated and the ovary "officially" becomes a fruit.
The stigmas, or female parts, of the flower don't become fully receptive until the flower opens. So pollination by insects isn't occuring until this time. I suspect that, if the flower is never pollinated, the enlarged, fruit-like ovary will not mature.
I hope this helps. By the way, if you are hoping to save seed from this unusual summer squash, you'll need to take precautions that the flowers are not cross-pollinated with other squashes. You might enjoy reading a book called "Breed Your Own Vegetable Varieties" by Carol Deppe. It's fascinating!
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