It's pin worms that human parents are looking for at night around a child's bottom, you can see them- about the size of human hair, but only about 1/2 inch. Much more of a problem on the east coast of the US (warm and humid), for kids who run around with no shoes.
If you take your kid to a Dr for itchy bottom, they can tell you all about pin worms. They might stick a piece of tape to your kid's bottom to pick up eggs. Or ask you to check at night for the adults on the skin.
NOT roundworms, the parasite often in chickens, and can sometimes RARELY show up inside of an egg. Most roundworms species are found in the GI tract, but they can get confused and be other places (aberrant migration). In heavily parasitized birds, they can be all over the place. A worm could end up in an egg the same way a 'meat spot' ends up in an egg, as the yolk releases from the ovary and travels down- it gets coated with the white, then the shell. If something happens to be in the tract along with the yolk- it will get packaged along with the yolk. Meat spots are pieces of ovary or reproductive tract that get packaged up accidentally with the yolk.
Wormy eggs are really uncommon, but do supposedly happen. I haven't see on myself (whew)