When Coera was ripped from Baod, he was left with a Coera-sized and -shaped hole. He maintains the hole, with the intent of someday returning her as his beating heart and engine.
When Eva was created – in the general shape of Zehn-Mehr – by the masters of brotherly harmony, Chomir and Sensihr – she was not intended to be the compliment of Adam (though a piece of himself was used to seed her creation for compatibility), but of Coera. She is the Earth Mother – the Governess of Creation and of Man in particular. She is a source or a doorway to Earth magic. And she preserves not only mankind, but the flora and fauna as well. She is chief ambassador to the Heavenly Assembly, and is a colleague of the Harvest Authority – the gods that control crops, forests, springs, fish-bearing streams and rivers (but not the sea).
That Eva and Baod are both locks which Coera fits is their one similarity, one that Eva works hard to ignore but which is often thrown in her face.