@SaphireE90 If you humour the setting and think from the lens of within the world, one might assume that the family resents her for taking the place of the one who was in the position previously, however irrational. Imagine your mother, father, sibling, or child died and your family spends (probably the equivalent of) tens of if not hundreds of thousands of dollars maintaining the facade that they never died. Moreover, you have to pretend in public that this stranger is the person that you've lost forever. It is also a constant reminder of your family's infidelity (though we don't know how many people outside of the father/mother?/brother? who know this).
However, a more likely culprit is the personalities of the characters themselves. They never accepted her, nor did they ever care for her; that is how they've been characterized. They ignore her and would rather have her die (and probably receive condolences + pity from the public) than allow for the possibility that the plebeian they took in breaks character after leaving the eyes of their household. She could easily reveal the secret at any time, and if she marries out to a similarly powerful house then there's nothing stopping her from doing so out of spite (it would probably get her killed or exiled, but it would be easy to add into a will or posthumous writing and then doom their entire family line).
There are definitely reasons for them to kill her off rather than allow a wild card to roam freely. Their willingness to do so coupled with their indifference tells us about them—if I had to guess, they also hate the common folk and those without power (i.e. MC prior to their need of them).
@scarlet_Summer Rationale for why it makes sense for them to kill her if they never trusted her above. It's also for characterization and indeed, to serve as the inciting incident that triggers a change in the MC's previously complacent attitude. I would not say she is an unreliable narrator either because she simply does not know the answer. It is not unreliable narration to avoid preemptively answering/spoiling plot questions the moment they arise without letting characters figure it out through their actions (if so, then there would be no mystery, cliff hanger, or plot twist to any story).
