This isn’t even a can situation. Except for those rare cases of two partners during together in an accident, one of your will die before the other. This hypothetical situation isn’t hypothetical, it’s the norm.

And immortality doesn’t change anything. One person dies and the survivor grieves. After some years, you get over it. Life goes on. It’s not that you don’t still miss the person, but life goes on, and the pain fades. This happens in mortal timelines, immortality doesn’t make the scenario any more poignant.