A client once said, "I barely recognized myself when I was with her. I'd never actually loved before, and it was exhilarating!"
We have opportunity to discover more parts of ourselves with each new person who comes into our life. Some parts we're familiar with, because we've expressed and exercised 'em before. Other parts are fresh and new to us, perhaps previously unearthed, and we get to be surprised and delighted OR shocked by 'em (how about that guy or gal who made you feel so angry, you wanted to put your fist thru a wall?).
We are typically a bit different around different people. For instance, are you the same, exact personality with ALL of your friends~ or do one or two of em somehow ignite your sense of humor, playfulness or sarcasm? Does anyone in your life trigger the practical joker in you?
All these various dimensions of yourself are YOU, they're just aspects that don't get to come out and play with every person you know. Aren't you able to go much deeper emotionally or intellectually with some people, than with others?? Is that really about the other person, or is it about your own personality facets that mesh and blend well with certain others?
So, when a love relationship ends, we can surely miss the good times we shared with that individual, but My sense is that we experience a greater longing for our own aspects that got to dance for awhile with that other person, but are now temporarily dormant.
Think of it this way: Perhaps they were the lyrics, and we supplied the melody~ or vice versa. The upshot? We made lovely music together for a time.
I believe this is part of why when even a tormenting or abusive relationship ends, we find ourselves "missing" the other. Never does it make sense to us, this painful longing we feel~ but it's why I have postulated that it's not as much about yearning for the Other, as much as wanting to connect once again, to the aspects in Ourselves they allowed us to recognize and experience.
That's My two cents, anyway. If it makes sense to You, so much the better. Just remember this~ you may have lost him or her, but you can't actually lose YOU, even though it may feel that way right now.
The upshot? It's pretty likely you're now acquainted with more dimensions of your Self, than you were before you met that person~ and that's ALWAYS a good thing.