STORY

Izumi and Meroko stay together since her death.
They started to work together as team, but Meroko fallen in love with him at the first sight. Izumi requites her feelings but that time he was too jelous of Takuto and too cold to admit that he was in love with Meroko.
It's Izumi that decides to destroy their team and that says to Meroko to be the partner of someone else: Takuto.
Izumi's rejection is the reason why Meroko became totally ridiculus with Takuto, thinking (or forcing her to think) to be in love with him, but from the bottom of her heart, she's always been in love only with Izumi.
The meeting with Mizuki cahnges Meroko's world and determination, because she really understands that she'll never have a chance with Takuto, that falls in love with Mizuki.
So she turn back to Izumi, but not as lover, only to ask to him to get Mizuki's life.
When she understands her mistakes, Mizuki and her become friends. And that are the moment in ehich Izumi understands that he's always been in love with Meroko.
Meroko is the only girl that makes him smile, the only one that appears in front of Izumi's mind when he's sad and wants to smile.
At the end of the manga Meroko and Izumi rework together as lovers and as team, in the anime is different because Meroko becomes an angel and she fly in Heaven, obviously without him.
Unluckily their relation isn't deep there, but we have to considerate the manga and the real, deep meaning that Arina-sensei made into of it.

PERSONAL OPINION

When I started to read Full Moon wo Sagashite I immediately loved Meroko, and with the development of the story I always supported her and Izumi together, because their relation isn't something usual for two heroes of a manga, it seems really a real one! Beacuse they're not idealized, they're two persons with merits and imperfections that sometimes can be evil, making bad actions. But they share something that nobody knows in this world: death. A destiny of death in life and in present.
They bacame half-shinigami and at the begin we can think that they just want to reach the final form of their new nature, but it's not like this, they're two souls that are searching for love.
Meroko's heart was bleeding for the delusion of the thing that she considered the betrayal of her best friend. Izumi thought he never knew what means to be loved by someone because of his mother.
When they were a team together and Meroko was in love with him, I would have never thought that Izumi was lying about his feelings and it's so touching when he went back on her.
Izumi hasn't an easy personality to understand, his character is very complicated, and Meroko too, because until the end we can't guess what could be their destiny.
But they're twin souls, I always thought that Meroko 's heart is that part that Izumi needs, and for her is the same thing. Yes, I think that two twin souls aren't two "same" souls, but two souls that can complete the heart of the other one, as if our heart would be full just for half, and the other part is made to wait for someone who can top up it with love.
And Meroko and Izumi are the most beautiful example of this theory, to me.
The conclusion of the story is simply fantastic, because they finally understand their real feelings for the beloved one, and they become a team again, partners that share not just a job but an eternal life.
It's sad to think that they're dead without knowing a person to love, but the eternal life is the most important one, and they share a brilliant future, a future where their hearts won't be alone more.