Ill Company

The Village and Pillage introduce the Bad Omen effect. I believe that slaying the Enderdragon should invoke a similar effect. The temporary name is Ill Company. Approaching an Enderdragon egg within the overworld and with Ill Company, triggers an event much like the raid. Waves of 'ill" mobs spawn seeking the egg. The player must protect it. I imagine the designs of these creatures as less shy siblings of the enderman. They want that egg and will take down whoever stands between them and it. 

The player wins if they protect the egg from all of the waves but loses once the egg is seized.