While I'm busy writing up the review for episode 4.08, here's a theory to occupy your mind. In the final scene of episode 4.08, the observer visits Olivia and gives her a dire premonition: He has explored every possible future and in all of them, Olivia has to die. The following theory belongs largely to SERIESOTP (on Tumblr) who proposed it in the first place.
Olivia can’t die because Peter will always try to do something to avert her death like what he did in the season 3 finale when he used the machine to go back in time and make another choice. In a recent interview, Joshua Jackson even said that once Peter finds out about Olivia’s premonition, he will do what he can to make sure it doesn’t happen. In turn, Peter can’t die either because Olivia and her abilities will always be able to rely on her love for him to bring him back (as shown in Subject 9). In order for Peter to properly fulfill his destiny (Death), he cannot have a connection to Olivia and cannot have known her which is probably the reason why fate has intervened time and time again to keep them apart (and maybe even the reason why they don’t remember their meeting as children, knowledge of which would only strengthen their present bond). Thus, three scenarios are possible:
1. One dies and other lives- In order for this to happen, their connection to each other needs to be forgotten or broken. This is probably where Lincoln comes in and why Lincoln and Olivia are “fated” to be together as opposed to Olivia and Peter (a pairing that beautifully defies fate, you could say). Peter could also sacrifice himself (again) and do something to severe the ties between himself and Olivia such that he dies, but she lives. I’m genuinely terrified that this is what is going to happen in the season (not series!) 4 finale. On the other hand, Peter’s actions could also ensure Olivia’s death in the form of a self-fulfilling prophecy- in trying to avoid her death, he may just cause it.
2. Both die- If both are unwilling to let go of each other, in order for Peter to be non-existent (dead) permanently, Olivia needs to die so that there is nothing powerful enough to literally tether Peter to this world. If no one intervenes, this is most likely the end result. It’s unfortunate since it means (as WRIGHTROAD on Tumblr said) that their love for each other and the fact that they “hold on” to each other will ultimately kill them both.
3. Both live- Right now, they are both co-existing, but it’s only a matter of time before the observers set their plans in motion and one or both of them die. But, something or someone could intervene to ensure that Peter and Olivia’s connection is not fatal and that they are both meant to live. Maybe that’s how September got wounded. I’m almost sure that he got shot while he was trying to save Olivia since that’s the only way to save Peter (which goes back to what September was trying to do in the season 4 premiere- for some reason, unlike the other observers, he believes Peter needs to live). It would be a really cool twist if it was the future Olivia or Peter that shot him (either intentionally or accidentally).
I would love to hear your feedback on this theory. Of course, I could be completely wrong (I probably am!).