Well, do we know if her parents died, vs. simply being 'abandoned' to the orphanage? If not, mom theory could live...
As I understand it, Elsa's parents shouldn't exist within the story, since the world's history and character backgrounds (the "lore") are dictated by the IRL game, and it describes Elsa as having no family, they might be dead for all we know, they're a non-factor. The actual events of the game have changed because of Evie's refusal to follow the system and Elsa going out of her way to follow Evie, so the future has the potential to change based on the girls' agency, but the past or the "setting" remains the same, so Elsa is still an orphan, so it's much more likely that it's future Elsa interfering with the system and giving the girls more freedom.
(Now that I think about it, this story has quite a lot in common with FF VII Remake lmao)