This death tore him apart, and he blamed himself. Elizabeth became the woman who inadvertently lead to Reiko's death, so naturally, the relationship was once again put on pause. The couple took some time away from each other after this reveal, but ultimately Finn and Elizabeth reunited. Of course, they started out as just friends, but their path was obvious. They had minor breakups along the way, which makes it feel like the fifth time giving this dead-on-arrival relationship another go.
To make things even more perplexing, "GH" is using Curtis Ashford's (Donnell Turner) shooting to push Finn and Liz again. First, they were thrust into yet another emergency moment together, forced to work together to save Curtis' life. Then, once Curtis was stable, instead of having them talk through their issues, work them out, or even acknowledge them, they are playing matchmaker between Curtis and his estranged wife, Portia Robinson (Brook Kerr).
To cover up the fact that Finn and Liz have nearly no chemistry and have fundamental issues in their relationship, they're having separate scenes where they try to convince Curtis and Portia to reunite. They're more invested in the drama of everyone around them, and that's why this relationship hasn't ever worked and never will. There's nothing wrong with them as people per se, but together, they're uninspiring, held together only by some sort of trauma in their lives.