@Isekaijin: Actually, I think you're on to something. Like you said, the grandparent lived a full life, BUT he also had a family. If that's the case, then it's possible Eve won't "die" but will still be around despite Tarou having a proper life and love with real people.
Unfortunately, while she's not a delusion, per se, she isn't real either. She IS a manifestation, just the only advanced one among a sea of FLZ. The fact Ibusuki was able to control her like a regular FLZ is proof enough. Tarou also has shown to have a bit of control over her too (though this only extends to what she wears now), but both Tarou and Ibusuki are against doing this anymore because they feel she's not some lifeless doll.
And no, there's no evidence that Ibusuki wants to eliminate Eve. There's evidence Tarou's dad does, but not Ibusuki. Ibusuki actually cares about Eve too, but my guess is she plans to put Eve to sleep somehow. Remember that Ibusuki views Eve like a sister, but has a complex about Eve's appearance because it's her ideal appearance. Also have to remember that Ibsusuki re-fell in love with Tarou and wants to get together with him, so leaving him out in the cold doesn't make a whole lot of sense. Ebino's was part-jealousy, sure, but it was mostly guilt since she believes she's the catalyst to Tarou's powers re-emerging (which so far, she is). In Ebino's case, she still doesn't fully understand what the FLZz are or who Eve is. Ibusuki does and while I don't doubt she wants to continue her mission of not seeing FLZs anymore, I seriously doubt she intends to deep-six Eve.