Self-realizaton
When 8 of cups come out as the outcome to a relationship reading, clarified by 3 of swords. Does this combo reek break up? Could it just be about leaving the past behind to be able to move forward with the relationship, and that this transition would not go totally easy?
8/Cups, like the 3/Swords can indicate a realization about the relationship that makes it not what one or both participants thought it was. It's one of the ignored definitions of 8/Cups that it can imply a kind of "wake up" feel. You were drunk and went to bed with someone you thought was wonderful, and now you've woken up, look over and go, "what was I thinking?"
Likely, this means that the participants in the relationship realize that the relationship just isn't working for either of them and they split. However, it could mean that the relationship, as it is, isn't' working for them. I could as easily see this for a couple where one of the participants realizes that they're gay (or their partner realizes it) and it's not going to work, as I could for a pair of close friends who realize they have to go further or break up. That being just "friends" isn't enough.
Similarly with 3/Swords where you learn something that pierces your heart, but also bleeds out ill feelings have been building up. However unhappy you are that this thing (whatever it is) is not working out, you also feel like you can finally move on and find what you're really after. You realize that this thing was holding you back, keeping you from developing and finding real contentment.
Which is what I find most interesting about these cards. They're less about the failure of something (like a relationship) as a person's realization of who they are and what they need to do or be or become. There is a "living a lie" or in the case of 8/Cups, "living in a false paradise" feel. What you were doing wasn't right for you, much as you may have wanted it to be right. There is freedom and a chance to be more yourself in this realization.