Glad you don't have an eggbound hen! I have a few answers for you.
If you give your hens calcium and avoid high egg production breeds like Sex-links, it drastically reduces your chances of eggbinding.
Eggbinding is fairly common among high egg production breeds. I believe that some hens get eggbound for an hour or two then get the egg out themselves at least once or twice in their lifetime. Young and older layers are most often the ones who fall subject to it, but every once in a while you might get a chicken who naturally has trouble laying eggs. In my experience, lice weakens the hens and causes them to go eggbound more often, and perhaps because they have two problems to fight against all my hens who had lice and were eggbound died.
If they are eggbound, your hen or pullet will hang around the nesting boxes, move slowly, look sort of like they are waddling, go pale in the face, have a pulsing vent, and you should be able to feel a lump near the vent which is the egg.
Most people say that after a few days the hen is doomed, but I have had a hen who got her egg out after a whole week. Sadly, Loyal Penny ended up dying two weeks after due to Lash Egg. I just care for them and hope, either until their egg comes out or until they seem to be in so much pain that I have to put them down.
While they are eggbound, you can help by putting a pinch of Epsom salt in their drinking water and giving them extra calcium. You can also give them Epsom salt baths and massage their back ends to gently try to push the egg out, just be careful not to crack the egg because if the eggshell cut the inside of the hen it could be deadly. Keep them in a warm, moist place (I use my extra bathroom). Most importantly, give them lots of love and spend time with them.
If you want to know more, there are a couple articles on BYC about eggbinding. Have a great day!