As for broken relationships, I'll run it through my personal perspective and experience:
Relationships are. Period.
A relationship is by essential definition the description of where two objects are in relation to each other in a given context. Thus, any description is purely positional.
I find it useless to add judgement values to relationships, such as good or bad, fixed or broken.
Adding a judgement value to something implies that there's an underlying belief that there's a right way, and a wrong way. In my eyes, this kind of categorization serves no purpose. Rather, it hampers the efficiency/flow of an interaction (keeping a person from being fully present in that interaction) by switching the focus to the narrative (fantasy) instead of the events of the interaction (reality).
That said, I do add personal values of whether - and how much - I like and enjoy various relationships. But it doesn't become a value judgement.
When someone tells me that a relationship is broken, needs repairing, or that they're working to fix a relationship - I often chuckle. True. Sometimes inappropriate? Sure.
The reason why I chuckle, is because of what these statements convey. In very broad terms: Their relationship is in a state where it's a game of position; it's just politics. That they're not personally present in the issue at hand, and likely not personally present in those relationships. That they likely don't really love each other, as they claim to do when sending excessive amounts of love-related emotes. I laugh, becasue the thought which comes to mind is; "Are you trying to convince me, or yourself?" Though it usually remains unsaid. (I only get to properly have this exchange with SEI friends, and a very close SLE friend.)
In some cases, it just means
"We used to have a good time, now we're not, so we're trying to get back to having a good time."
In those cases, I rather listen to what follows. Sometimes I laugh, but that's because what follows sounds incongruent or seems insincere.
So perhaps one can say that I don't know how to repair broken relationships - but it's not because I
don't know how, rather it's because the notion of a broken relationship
is inexistent/irrelevant in my mind. I just analyze the current state which the relationship is in, and work from there.
(Incidentally, this is the kind of understand people come to through their involvement in polyamory or relationship anarchy, where they unlearn the societal expectations around relationships.
Fe)
Hope the perspective might shed some light on your own path/research.