I'd say it's safe to assume that news of the firing had already made the rounds. I don't think it'd have been rude or out of place for her to tell the others, either - on the contrary, it would have been the responsible thing to do so that the others will be able to handle the fallout that she's unable to. She knows that the others will be able to support her better than she's capable of.
All in all, I think Dora's handling this rather smartly, and dare I say, considerately. She's helping in likely the only way she knows how, without sacrificing her ability to keep detached and avoid being seeped in the toxicity that is Faye right now. She's likely not in any emotional place to deal with it, especially considering her recent severing of her ties with Sven. That she's willing to delay the paperwork so that Faye won't have to pay out for her care shows that she does does still care for Faye, but recognizes that the appropriate thing right now is distance. Everything's still raw, and she'd likely cause more trouble than good at this juncture in trying to insinuate herself in Faye's recovery process, nor would she want to be considering the situation. And it appears that she's sorry that she's just not capable of being a better friend at the moment, with a dash of guilt for maybe feeling partly responsible for the current scene. Which is unwarranted, imo - Faye would have hit bottom eventually, it'd just have been a different catalyst.
I'm willing to bet that after some time has passed (likely a good deal of it), that they might one day be able to come back together as friends. but both, and especially Faye, need to resolve their issues before even attempting that.