[quote=@harinezumikouken]
In the Marine Corps, one of the reasons that we are such a strong fighting force is because of misery. As a group, you suffer and endure misery together. You may end up hating this one fucker's guts at first, but through trial by fire, he becomes a brother. An unbreakable and eternal bond that follows you wherever you go in life.
[/quote]

I feel a potential bond of this nature between Sapphire and Shiro is undermined by the fact that Shiro is setting half the fires and Sapphire is often the one getting burned.

Is there a Japanese term for "Character who is initially hostile but as she is injured accidentally over and over and over and over and over again gradually grows to appreciate the person nearly getting her kill"?

Unless there's an anime trope for that I think Shiro is out of luck.