Ok, megan, so I had to reborrow to make sure I wasn't talking out of my arse about 5th Wave, but here you go. Note that I have only read the book and not seen the movie.
In the book, the character Evan *is* the sniper who shoots Cassie. Basically, he's a Silencer who is supposed to kill her. He is tracking her to do so, sees her in the woods, sees the stuff with the Crucifix Soldier go down, basically stalks her instead of finishing her off. He goes to kill her...and then doesn't. And then having not done it, finds it increasingly harder to do so each time he gets the chance. He continues to stalk her, reading her journal, etc., eventually falling in love with her, more or less as a reason to justify to himself why he didn't kill her initially. He loses track of her, finds her again, and this is when he shoots her. But he, uncharacteristically, doesn't kill her. He waits for her to come out from cover and run. Except she doesn't run. She confronts him, and instead he runs. She would have died from her injuries, but he then takes the not-killing her a step further into saving her.
For her part, Cassie basically has killed the last person she's seen, at a point when she speculated she might be the last person alive, before meeting him. She's utterly reliant on him initially while he nurses her back to health, and she comes to the relationship considerably more reluctantly. She knows she can't trust him, but yields to, I think, the basic human need for companionship under duress. Then as events reveal that she is right not to trust him, she ultimately leaves him. He follows, and she finds herself relieved to see that this is the case, but the complexity of their background is never lost on her.
So, in my view, unlikely, but not completely unbelievable. Is that helpful?