First of all, I'm really bad at remembering things correctly, so forgive me if my description s*cks.

There was this boy who tried to save a girl that was fighting a monster. But because of that, the boy either died or became infected with a monster virus (I don't remember which it was). Then there a monster hunter and since the boy was now infected/dead and would be turning into the same kind of monster, the hunter wanted to kill the boy too. But in the end the boy could convince the hunter not to kill him and to take him along. The hunter agreed, saying that he will kill the boy as soon as he starts to turn into a monster. I think the first sign of becoming a monster was craving raw meat.

I hope you know what I manga I mean. Thanks in advance! ^.^

That sounds super familiar and I think I might have read it too but I can't think of the name either. I'll let you know if it comes to mind.

Not sure, maybe Immortal Regis

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I have yet to watch it but it sounds kinda like Buso Renkin

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Smiles Conceal Knives - Lynn Flewelling.
There is No Such Thing as BAD Words.

In Busou Renkin, the mc never craved for flesh...In Immortal Regis the mc became an undead, so it might be possible..

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I checked out the manga's you said, but it's neither of them. I think I remembered something else about the story. When a hunter kills a monster, then it leaves a small toy-like(?)version of that monster, the size of a hand. I remember a hunter who picked that up... Any new ideas?

I'm absolutely sure that's kurozakuro

Kurozaka is similar but the MC didn't become a monster trying to save a girl; he became a monster when a glass orb went inside his mouth. The rest of the info such as that of the hunter is correct though. You sure he became a monster by dying and not blending in two different mangas?

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No, you're right, sorry ;P It's Kurozaka. I mixed things up again. I'm bad at remembering stuff.