Is it intentionally ambiguous as in they didn't want to commit to a true ending or are they both alive?
Well, Hei is alive, that's for certain; however, what happens to Yin isn't entirely mentioned.
One thing that could prove that Yin is dead is because on near the end of the anime, Yin appears (the one in the white suit) and asks Hei to kill her, in which he agrees. In the OVA, she also says her final goodbye and confesses her feeling for Hei.
However, in the OVA, Izanagi does say that he'll grant Yin's wish which would be to be with Hei, and Izanagi did grant July's wish to be with Suou.
Also, Bai's power allows for molecular manipulation. It is how Hei is a Contractor since she fused with him near the end of Heaven's War and how the plan to destroy all Contractors by destroying Hell's Gate failed and how Heaven's Gate cannot be touched.
At the end, Bai's star which disappeared because Bai was trapped in the Meteor Core began to shine again because she was released. If Hei got Bai's power back, then he could have fused with Yin as well and (if a third season is made) is now trying to find a way to reverse the fusion so that Yin can return to her body (maybe also to allow Bai to come back). However, that is speculation, one thing I've read that while Hei is holding her body, it's glowing, which could mean she's alive, though I didn't actually notice.
I should point out that what we see is a light growing brighter when he puts his hand on Yin at the end. While he could be killing her here, the light could be the same that Hei emitted when he made Anti-Gate Particles nonexistent at the end of the first season.
Hei is alive, and so is Bai, who is fused with him.
Now there are two explanations:
The first and the best one is Hei was not able to use his powers as Bai fused with the core, and not only that but at the end, the core is destroyed, bringing Bai back to Hei. Bai had a matter-changing power that could allow Hei to remove Izanami from Yin, as she glows, there is also the answer by Memor-X talking about the Anti-Gate Particles, but I don't believe it. His star also shines brightly, which happens when the false star is in action, so Darker than Black is uncovered.
Another thing is, he could be shocking the spirit or whatever, and as he is doing it, Yin is dying. He is carrying the body at the end to her grave and Shion must've tried to satisfy all by making the boy at the end, as you know, when he was trying to make himself it became, Suou. No Suue or Suo, or just Shion's sister, male to female, so when he tried to make Yin, the reverse process took place, and it was touched with Izanagi. So it tried to kill everyone, emotionless, it was like a doll. She can die like Huang.
So at the end, Shion must've made a clone of Yin which is Izanagi and Yin herself is Izanami, the white one, so when those dudes are gone and their glowing hair and they become Yin and the mysterious boy, Hei will try to kill him in the third season, or Yin is alive and became into the heartless doll, or just became into two.
Well, just wait for Darker than Black: Gemini of the Meteor.
If you want, skip to the Conclusion below.
So it was the prophecy to which if Izanami and Izanagi met, they will give birth to a new being, a one which represents the two gates: hell and heaven. That creature at the end is the same being I was talking about.
Through the series, it is known that Yin had become Izanagi (which the OVA was about). So at the end of the OVAs, Yin fulfils her job and transform into Izanagi. Thus, the organization Hei works for (a.k.a "syndicate") is doing all it can to prevent Izanami meeting Izanagi and simultaneously trying to find another solution in case they meet: that solution is the brother in the wheelchair (Sue's brother) which he can basically copy-paste anything he wants; he is a contractor. So, he is producing more beings like him so they could copy Earth faster.
However, there is one problem, the ME which is a device meant to erase or adapt memories into beings can only "tape" a memory that will stay within the being for 3 days at its maximum. Therefore, they use a meteor fragment (found at season 1 in one of the episodes which Hei took under the syndicate's orders. I believe it was used in season 2) which can contain the being's memories until the fragment is cracked or broken. To test their theory, they create Sue (the girl in season 2) which was the sister of the wheelchair contractor and creates memories for her into the meteor fragment, which is believed he will make sure her memories will bond to her till it cracked. Near the end of season 2, it seems the theory is correct that the meteor fragment will contain the memories.
So by multiplying the wheelchair contractor, they recreate Earth: a new world without any contractors or dolls, and save all the humans' memories in a big fragment (that orange thing you see in the end, that thing has at the same room all the wheelchair copies). So, in case something will happen to the real world, they make sure humankind will survive.
With that all discussed, what happened with Hei? In case you didn't know, Hei lost his power, and with the meteor fragment of Sue, he basically delivered his contract power to her (that's why she became a contractor). Hei doesn't have his power until the end when he meets Yin as Izanami which returns Hei's powers (the scene where Sue dies) and Yin gave Hei two option:
- To kill Yin and prevent the birth of the alien which might erase all humans and contractors as one; saving the earth, or
- To use his power once again to separate Yin from Izanagi; by doing so he makes sure Izanami and Izanagi will meet and will bring birth to the demonic child we see in the end, the one sucking souls from anyone; using Hei's power, he will be able to get Yin and to live with her till death will be shown upon them, which might happen in the next future.
Hei chooses the second option, he gets Yin and the real Earth isn't safe anymore. So when you see Hei holding Yin and going with her, you should know she is alive and he is as well. Meanwhile, the demonic child is on earth, Americans conquer Japan, the syndicate continues his affords to prevent from everyone dying and there is another planet earth with humans only on it.
Conclusion: Hei uses his power to separate Yin from Izanagi and by that, he gets Yin alive. Earth is being duplicated but without all this messed crap. Syndicate continues to save humanity on the fucked up Earth - the policewoman is working for the syndicate.
Btw, Sue was only an experiment tool to see if the fragment can hold the dull's memory.
My opinion is simpler. The main topic of the second season is "copies" or, better, "clones". Copies of sex and character opposed to the original, but with the same power and memories.
Yin is the most striking example. Yang is inside her. She represents Ying and Yang, the two opposite eternal and primary, without which world wouldn't exist. The last scene shows Hei carrying Yin's body, that body which is now an empty shell. Hei looks at a star falling from the sky. A contractor is dead. I believe the dead contractor is Hei. He lost his power, those he loved, and if we exclude Yin's research, he is forced to work for others without being motivated. In the end, he must also kill Yin, the woman he loves. Why should he still be around? I think he dies together with Yin.
In my opinion, copies of Yin and Hei were created with same powers. Basically, in the end, we witness the birth of a new syndicate, with "old" faces. So, for me, it makes sense there are clones of Hei and Yin. Mao also has a new body.
Another explanation could be that during the OVA, Yin told Hei that one way they could be together is when they become one, while she hugged him in the white form, which could be referred to his particle manipulation ability which could be used to fuse them together just like Bai and Hei did.
Regarding Izanagi's words where he said (in last OVA's last 10 minutes) that he would grant Yin a wish when Hei arrives, I suspect it could be that he makes Yin's body human so that one day Hei could reverse the process of the above-mentioned fusion and bring Yin to her now converted Human body,
he granted a wish by giving a human body to Yin but instead, it turned out to be a boy (which is due to Shion's ability's flaw that the copy he creates has one major difference) and now Yin is forever fused with Hei as the bright light of Hei's particle manipulating power indicated at the end of season 2.
I think Hei did kill Yin, and I believe Izanagi was never revealed in the Anime. If he didn't kill Yin, then he's hiding her somewhere. Izanami is an anti-contractor weapon with Yin inside, and Izanagi is never truly revealed except for that little extra bit at the end of the episode.
We do not know for sure if Hei did or did not kill Yin, and if that boy is in fact, Izanagi, I'm assuming Hei will come back, or the new "Syndicate" will try and kill him. He's probably and Anti-contractor weapon as well from what I see. But anyway, I think Hei killed Yin, and if he didn't, she's probably more human than a doll now, since she changed a lot in the OVA's.
But since nothing is proven yet, all we have is this picture: