The so-called 'stuck egg' is when the hatching time has arrived, but the dragon is still stuck inside the egg. At this point, a giant dragon would already have passed five hundred years of its incubation period, possessing a complete consciousness and even able to communicate with its parents outside of the eggshell. Yet, they can't break free from the shell.
Some might suggest: why not just break the eggshell?
This brilliantly clever idea was surely tried by the giant dragons. As a result, they got a mentally deficient or even unconscious juvenile dragon, as if the dragon's soul was shattered along with the eggshell.
That is to say, unless the juvenile dragon leaves the eggshell on its own, even if it can call for its parents through the eggshell, it will still remain stuck. This is the so-called 'stuck egg'.