Sounds like the aberrant sorcerer origin: You were implanted with a mind flayer tadpole, but the ceremorphosis never completed. And now its psionic power is yours. When you use it, your flesh shines with a strange mucus.
Combined with a bit of Netherese meddling (with a precedent in Ioulaum's transformation into an elder brain lich while preserving his mind) and a splash of quasi-divine intervention, and you've got yourself a potential for half-illithids.
After all, the Netherese Ioulaum both created the first alhoons and illithiliches, and also found a way to turn his lich form into an elder brain.
I cannot imagine this is intended by the elder brains or illithids at all...their single greatest fear is creating the Adversary...a boogieman story for illithids which predicts that one day there will be a mind-flayer who will fully retain the personality of the host and that he will be the one who will bring about the end of the illithids. They fear this so much that they kill any mind flayer who displays any inherited habit or nervous tick from the host and those who inherited such a thing have to be very careful to hide it because if they are found they'll be killed. There is n way this outcome is what the illithids signed up for when they allied with the dead three and probably Shar as well, since her shadow magic is in play and her shadow magic cannot be used without her permission.
