The immortality/mortality tension is a big theme in Tolkien, as well as much of modern fantasy. It is most easily seen through human-elf romances. Although there are several throughout the legendarium (only three of which ended up in a union), I will be focusing on the most famous one, where this theme is most evident: Aragorn and Arwen.
As the film shows, Elrond fears for his daughter, thinking she will hate life after Aragorn’s death. I believe this is much more evident in Elu Thingol, Luthien’s father from the First Age. Or maybe he just hated Men. He charged Beren with the impossible quest of prying a Silmaril from the Iron Crown of Morgoth. Likewise, Aragorn was charged with becoming the King of both Gondor and Arnor.
After Aragorn’s death, Arwen mourned him, stayed in Gondor for a couple of years, but eventually left to Lothlorien, and lay down on the hill of Cerin Amroth, where she first met Aragorn. She had given up the Twilight, or the immortality of the Eldar, to be with Aragorn, so she does age, but lives like the Numenoreans, with extended lifespan and the grace to choose her moment of parting, like Aragorn did in the end. She essentially chose him over her kindred, and from that moment, there was no going back.