Savior
How Kureno becomes Rin's savior.
Kureno rarely interacts with anyone outside of Akito but Rin, by chance, happens to walk by as he's talking to Tohru. While she doesn't actually hear any of their discussion, she does see Tohru on her hands and knees on the ground, sobbing. She figures that Kureno said something unnecessarily cruel to Tohru and decides to chase after him and scold him for what he's done to her.
Much later, Kureno is walking in the Sohma grounds after dark and sees a handmaiden delivering food to the cat's room. Curious, he returns later to intercept the maid and ask why she's bringing food to a room that's supposed to be prohibited. Kureno continues to press the servant, asking who's locked in the room. The servant is so afraid to answer Kureno at all that he's able to figure out that Akito is responsible. Kureno tries to calm her down and tells her to give him the key to the room; she can say that he forced her if necessary. Crying, the maid tells Kureno that "she" hasn't eaten for days and if it continues like this, she'll die.
Kureno opens the room and finds Rin sitting lifelessly in the corner, hidden in the shadows. Chunks of her hair lay all over the floor. Kureno carries her out of the room and calls for a car to take Rin to the nearest hospital. He then makes his way to Akito's room to find Hatsuharu there; Haru is demanding to know where Akito is keeping Rin and Kureno tells him that she's been hospitalised. Outside of Akito's room, Kureno confronts Haru and tells him that he'll be able to see Rin in a few days and that Rin's first word when she was able to speak was "Haru." He also tells Haru that he and Rin should leave and never come back, for their own sake.
Analysis
My opinion on their relationship.
Rin tells Tohru that she doesn't trust Kureno and that he doesn't feel like he's one of the zodiac. Akito had always kept Kureno separate from all the others because she was afraid that they would find out that he was released from the curse, yet in some way, they had some intuition that something was different about him. As a result of Akito keeping Kureno separate, Rin never really got to know him at all and likely didn't interact with him very much.Despite Kureno being freed from the curse, Rin seems to remember him picking her up without her changing into a horse. She is hallucinating so her recollection is questionable, but if she is remembering correctly, it means that they still have some kind of connection with one another as members of the zodiac. Regardless, Kureno is clearly intent on risking his own safety to rescue Rin; he does it despite knowing that Akito will likely become violently angry at being interfered with.
When Rin is recovering from her ordeal, Haru says they should thank Kureno for saving her. We don't know if they talk to him or not but I would like to imagine that they grow to be friends in some capacity. I figure that since he's Uotani's partner (and Uotani being one of Tohru's best friends), they would end up spending time together through Tohru.