In the anime, there is a touching scene between Subaru and Rem. But according to a person who's supposedly read the light novel, the producers changed this scene.
In the light novel, Rem faked her death (she pretends as if she was dying in Subaru's arms) with the goal to hear his deepest feelings for her. Subaru really confesses his feelings for Rem and shortly after he realized that she was only playing.
Here's a link to Amino Apps about the summary where I've got this information: (it's pretty much at the end of volume 7)
Does this really happen? (somehow I just can't get rid of the feeling that this summary isn't trustworthy)