That’s a soft shell egg, my hens would pop those out on occasion. Can’t explain the cross, tho. These eggs are very soft and pliable when they slide out, it might have got pressed against something.
That is indeed a soft shell egg. And it may also be a hoax or a joke being played on this couple.
Back in high school science class we did an experiment that produced these same results. Each student put an egg in a cup of vinegar for one day and the shell became soft. We then took our eggs out of the vinegar and placed them on a shelf on top of a small object. I used a nickel and one girl used the cross she wore.
A day later the egg shells had hardened again and embossed on the bottom of the eggs was the inverted shape of what we had placed them on. My egg with the nickel under it had a round indention that when I rubbed it lightly with a pencil, you could see a crude resemblance of Jefferson. The girl who put her egg on the cross had an egg with a perfect indention of that cross.