So what I'm getting here is that the sword was a living thing, something like Fi from Legend of Zelda: Skyward Sword (except without a physical avatar body...maybe). When it sacrificed itself to save the ML, the blast killed the sword's "soul". Perhaps because of its sacrifice, the "soul" got to be reincarnated as the FL and live an actual life. Meanwhile the ML probably got the sword fixed and became attached to it, but since the "soul" left the sword, it's most likely just a regular weapon. It's like dating a corpse, there's nothing there anymore.
So to sum it up: Sword was alive, sword died and got reincarnated, its owner is in love with sword's dead body, and 100% tried to bang it at some point. Okay maybe not that last part.