In order to have a partially formed chick, the egg would have to have been incubated under a broody hen for awhile. If you do not own a rooster and/or collect your eggs daily (and they aren't scattered 'whither and thou' by free rangers, than it would be pretty impossible to have a partially incubated chick.
The thing about 'home grown' eggs is that they aren't electronically candled, etc. to be sure any 'irregularities' that occur normally in the production of eggs by chickens have been removed. Eggs vary in color, size, construction, shape and shell strength due to many different factors. Sometimes blood spots or other abnormalities occur, though not common. People have become accustomed to the sanitized and sorted eggs available at your local grocer.
I HAVE opened up partially incubated eggs ... it's a bit gross, but I toss the egg and don't bother my brain with thinking about it overmuch.