One thing I've considered for a good while now is that the possibility that Hiyori could be the reincarnation of Yato's very first shinki, Sakura. The series did state a good while back that that's something that can happen for humans. It could also play into how the series had Yato & Hiyori connected to one another by fate itself. Sakura did behave in a way pretty similar to Hiyori back when we saw her. The last interesting comparison is that Sakura's form was that of a koshigatana, a short bladed katana. With Hiyori's also being the same (not the exact same appearance though).
I have a couple ideas for how things will play out for Yato & Hiyori. Based on the way the series as well as Adachi Toka have handled Hiyori as a character, it would go against the narrative they've been going with all this time if they actually do just have Hiyori die, and become a permanent part of that world. Especially with the lesson she's learned throughout the entire series being to love and cherish the time that she has while she's alive. Also considering how Yato needs her to take his father's place, so that he doesn't disappear after killing the guy, it would definitely be a bad ending if Hiyori's dead.
The first idea I had was that just like how Yato's dad died but managed to return to being a human, gaining a lot of powers as a result; with him able to continue being reborn as a human while retaining his identity and so on, it could be a case where something along those lines happens to Hiyori. It would also solve Yato's problem, where the two can always be together, even after she dies, without him having to worry about disappearing, with her always existing in one form or another to be there for him.
The second idea (part of which seems more likely) is that Hiyori will for whatever reason be fine. Considering we only got like 2 chapters left, the author doesn't have time to drag this out. Normally humans lose their memories when they die and become shinki, but Hiyori isn't exactly a normal human. I do think there's a good chance she'll keep her memories. Also between Yukine, as well as all the other shinki friends she made (the grand majority not knowing about the gods greatest secret) would know her name, with it taking just one of them to accidentally call her by her actual name.
I do think Hiyori will likely be saved, more likely than not by the intervention of the goddess Amaterasu. Amaterasu does seem to have some feelings towards Yato and his group, considering she did show up out of nowhere to tell Hiyori and the others how to save him from the underworld. If Amaterasu has something up her sleeve that would save Hiyori.
If not Amaterasu, perhaps something happens with Yato's father, perhaps Hiyori has a connection to that woman he loved and not Sakura. It would seem incredibly random and kind of half-assed, but if he decides to do something to undo what happened to Hiyori, and allow her to live again. One last idea I had (which is a bit of a long shot) but going back to the Amaterasu idea, perhaps in exchange for saving Hiyori, Yato is to give up being a god, as a price or as a request. If perhaps the series ends with both Yato and Hiyori as humans, with Yato no longer having to worry about disappearing. This would allow the two to be able to spend their lives together as a proper couple. As for Yukine, he'd probably just get taken in by Bisha and Kazuma.