Imo Kim probably dies
Shes never brought up in Breaking Bad at all as we all know, i mean i can't picture her never coming back into Jimmy's life again in Breaking Bad, he seems like the only person shes close to and has no one else. So whenever he becomes Saul and gets his office as a criminal lawyer i find it hard to think she'd never come around him again at anytime.
She has to die in some way imo, perhaps her death is what drives Jimmy to become more and more Saul since she is really the only person left who cares about him. Once Kim's gone who's he got? No one.
I just don't see some argument or something driving Kim away from him for the rest of her life, i just don't see what he could do that would make that happen.