I don't believe that Hikaru and Hana end up as actual lovers in the end. Hikaru seems to view Hana more as a child than the goddess she has been idolizing without truly knowing her.

The guy burned the papers because he might realize that Hana may not love Hikaru as much as she does, or that she might come back. When he looks at the letter, he sees that Hikaru erases “I’m off” first instead of “goodbye.” This might be a translation issue, but the letter also doesn’t really indicate that Hana is leaving for good. She says, "I don’t think I’ll be back," and she looks back at the sea where the ring is. It seems she is okay with leaving because she doesn’t want to be one of the people who abandon Hana after discovering that the person she has been stalking isn’t what she is. I mention "stalking " because I’m pretty sure Hana didn’t make the first move to seek out Hikaru.

As for Hana, I think she is supposed to be misinterpreted by everyone. People believe she is this manipulator/toxic GF, but honestly, she is just a kid who has no idea what she is doing or saying. Hikaru, after living with her; describes her as a child even. It looks like she can barely take care of herself.