not explained yet. Based on the source material and the title being "Last Encore", I'm assuming it's the previous war's ending where nero and hakunon lost. Then fast forward to the current one where the male one exists and summons nero again. That's probably why it's called Last Encore, it's Nero's last encore/2nd attempt at the war after losing the first time.
Literally the very first scene of the fate extra anime is both hakunon and nero getting killed by the last boss of the video game source material. Hakunon is seen bleeding on the floor with no legs and a hole in her stomach, while nero fights the boss and eventually gets killed herself when she also gets a hole blown in her stomach.
I mean, I thought the whole crickets sound effect thing in reply to the multitude of same-sex parents in anime was a telltale sign but I guess not? Sorry, I really should stop with the whole sarcasm thing when people are riled up.
It's not like they act like a family unit or do family things throughout the show; it's not explicitly stated to be one after all. That kind of portrayal is definitely pointless too; I mean, why settle for this implicit nonsense if you can watch a multitude of other anime with the same kind of dynamic featuring characters of the same-sex?
Let me get my crickets for that truly explicit™ silence effect.