Heejin's relationship with Olivia Hye is one of the most mysterious things happening in the Loonaverse. 

The first time we got to see them together was at the end of "Egoist", Olivia Hye's solo debut, by that time the original theory was that their meeting marked the end of a cycle, the union between the beginning (Heejin, first girl) and the end (Olivia Hye, last girl) but this theory explore their relationship a little deeper from there. 

For those who are new to the theories, Egoist explains the runaway of Olivia hye from the Eden after being left behind by the rest of the YYXY members, on the video we can see Olivia making her way up the stairs through the different levels of my building, each level representing a dimension which Olivia had to go through in order to reach the other members. At the end of the video we can see Olivia standing on the rooftop and there is where she finally meets Heejin, this marks the starting point for this theory. 

Before we continue with their relationship is important to understand where Heejin was at that moment, from where I see it, their meeting on "Egoist" wasn't actually the same dimension where the other girls were (Let's call it the "A" part of the Mobius strip) but one of the many variations there's on the Loonaverse. On different videos before we've gotten to see the representation of the multi-universes involved on the developing of the story-line, such as the scene of Heejin's solo Single "ViViD" where she seats in front of a mirror and we can see 3 reflections of her, each being a different version of her on an alternative universe... for me on of these alternative versions of Heejin was the one standing with Olivia at the end of egoist. 

With that explained let's move forward; In Olivia Hye's debut album we find a B-side featuring Gowon and Heejin titled "Rosy", on the description of the song we read it tells the story of  the relationship between the first girl, Heejin, and the last Girl, Olivia Hye. Let's check a few parts from the lyrics: 

"Rose petals tinted red
Bitten by your lips
Slowly melting
Feel this moment" 

"You'll fall even deeper
Further and further you will" 

It's obvious for me at least that the lyrics have a romantic tint over it, now this if where things escalate.  

When Olivia Hye finally gets out of the "limbo" at the end of her solo video, Heejin is the first face she's seen other than Jinsoul's during the time she went through the dimensions to leave Eden, this make her feel a connection towards Heejin. Olivia has to keep moving from universe to universe to reach the "A" part of the Mobius strip where the members of YYXY are (Represented in Hi High) that's why she has to leave that version of Heejin behind, nevertheless she somehow manages to look for Heejin on every dimension she passes by in order to keep her connection with her, that's why Heejin, just like Vivi, is related to one Eden girl. 

From Hi High to the X1 teaser of BURN we can see a new side of Heejin where she have the power of fly and you might wonder, From where did Heejin get those powers? Let's remember Jinsoul is connected with Olivia because to help her finally leave the Eden they mixed their powers (Lyrics of Egoist) and then Olivia ended up with a part of Jinsoul and vice versa, with Heejin is a similar case but her connection is not with Jinsoul but with Kim Lip. During Hi High we get to see Kim Lip and Heejin together and then we see Heejin flying at the end of the video, then we get to see them again in “So what” as a team. 

After getting a piece of Kim Lip's power Heejin is allowed to explore the different dimensions and that's how finally Olivia Hye reaches the original Heejin before even getting into the "A" side of the Mobius strip that leads us to Heejin's teaser on the BURN era where she's flying on her own, for me this symbolized her attempt to reach Olivia Hye before she finally meets the rest of the members, there's where the last we've seen from the "A" side of the Mobius because since Butterfly both So What and "Why not" are both focused on the variations of the different universes. 

This relationship explains why Olivia Hye appears on Paris during Butterfly out of all the other places to be, Heejin is the only member who's related to Paris on the theory, she's looking for the original Heejin as soon as she reaches the "present" dimension. 

Heejin now with the power and becoming a part for Olivia and Jinsoul's team represents a danger for both Kim Lip and Sooyoung who's trying to stop Jinsoul and Olivia from hurting Vivi even more, that's why we see Heejin alone during "Why not" because she's not longer friends with the rest of the members just to keep her relationship with Olivia Hye going on the theory. (Her scene with Hyunjin representing a different time and universe that could be focused on the past where they had a relationship or a universe where Heejin never became a part of Olivia's plan to being with)