Board Thread:Questions and Answers/@comment-25588560-20161205235417/@comment-27701762-20161206002343

It is suggested that the other children could save in some capacity. If you restart the game after telling Toriel whether you prefer butterscotch or cinnamon, she will guess what you had previously answered. If you tell her she guessed right, she will remark on how whenever humans fall in she feels as though she already knows them, like they are old friends. Which suggests that they, too, met her, told her their preferences, and were able to reload or restart.

The question that then stems from there is why they died. There hasn't been anything clear, though I tend to prefer that while they had some capacity to reload, it was ultimately limited, and thus they could not essentially abuse the savel/load feature in the way that the protagonist can. This distinction would be linked to the red soul, which is surmised to have determination as its key trait, and since determination is what causes entities to have control over the timeline, the extreme amount of determination within the red soul grants the protagonist a greater degree of control than any other type of soul.