"An egg travels down the oviduct pointed end first. When it gets to the urogenital chamber of the cloaca, it turns end for end so it will come out large end first. Sometimes an egg gets stuck. The egg maybe too large( for example, if a pullet lays unusually large eggs,) or if a disease may cause the oviduct to swell or it's muscles to become partially paralyzed. The stuck egg then causes future eggs to accumulate behind it, distending the hens abdomen. Unless you can get things moving again, the hen will die. Lubricate a forefinger with mineral oil or KY Jelly and insert it into the vent. With your other hand, push gentlyagainzt the hens abdomen to force the egg toward the vent. If you can see the egg, but it is too big to pass through the vent, punter the shell and remove it in pieces( with great care not to let a sharp shard injure the hen). Rince the cloaca with hydrogen peroxide.
If the egg was stuck in the cloaca for to long, cloacal tissue may protrude through the vent. In that case, protect the hen from cannibalism by isolating her until her muscle tone is back to normal."
From the CHICKEN HEALTH HANDBOOK by GAIL DAMEROW
