On the topic of apologies, one can apologize without actually having done anything "wrong" or "bad". In those cases, it's an, "I'm sorry that my actions hurt you," sort of thing that can smooth over hurt feelings. Like, if your phone dies and you miss a text message from a friend, you might say something like, "I'm sorry that I missed your message," to acknowledge that the person might have been upset that it seemed that you were ignoring them or that they were inconvenienced. I do this often. It's not because I think I've screwed up so badly that everyone hates me or anything, but because acknowledging other people's feelings (even if I'm justified) helps keep friendships together and helps us see each other's points of view.
I think that's more of the apology style that might smooth things over between Faye and Dora. Whether or not that's a meaningful thing to either of them, I'm not sure.
I think it would be meaningful to Dora, but not necessarily to Faye. I think your premise is more or less what Dora was thinking when she sought Marten out after her date with Jim. She was not sorry for ending the relationship, but she was sorry that her actions had hurt him and made him feel ostracized from the CoD group. The thing is, Marten has a personality that is receptive to that, coupled with his own in-comic expressed relief (to Veronica) that his relationship with Dora was over. He was happy to accept Dora's olive branch because they had been friends before they got together, he liked CoD, Faye was there, and he didn't necessarily want Dora and himself to go through life hating each other much like with the girlfriend he moved from California to Northampton to be with.
Faye is much different. Whether she just has an "average" life making widgets somewhere, getting old, possibly marrying someone and having a family or becomes the Annie Leibowitz of the metal sculpting word, part of her (and this is definitely just an opinion here) will always resent Dora for taking this step. When Dora told Tai that her continued friendship with Faye was "up to her," that was Dora displaying a sort of insight I don't think she gets much credit for. Because of Faye's background, she is very quick to read situations as people abandoning her or being disloyal. I suspect the meltdown of the Angus relationship was not necessarily because he got the job but because he went for it in the first place. Yes, she encouraged him, but I really feel that deep down, Faye resented that Angus would take any step that may lead to her being out of her comfort zone, even if it proves to work in her favor down the road. I think we are seeing this with her feelings toward Dora. Faye might privately, or even to Marten and/or Hannelore, some time down the road express that getting canned from CoD was the best thing to happen to her, but I don't think she will ever completely forgive Dora just as Dora couldn't completely quiet her suspicions that Marten wasn't over Faye.
I do think that the Faye/Dora friendship is moribund. They may say hello and even hang out every now and again at selected events (possibly at Claire and Marten's engagement party or Steve and Cossette's, whichever comes first), but I think just as the last Angus strip, which also ended with Faye being in an empty CoD, indicated the severing forever of that relationship, we have seen the end of Faye and Dora as buddies.