EMD could potentially stand for many things in the context of world fiction. It might be an acronym created by a particular author for a unique concept in their fictional universe, like a special organization, a type of magic, or a technological device. Without more context, it's hard to be specific.
If EMD is a key element in a fictional world, it could play a role in driving the plot. For instance, if it's a powerful object, characters might fight over it.
The Beginning After the End manga has indeed finished. It provided a satisfying conclusion to the characters' arcs and the overall narrative. Maybe there'll be spin-offs or related projects in the future, but for now, the main story is complete.