As a boon for his efforts for Shar, Ketheric gains immortality from Aylin's situation.
Though, it's clearly not Shar who provided the immortality to Ketheric. Since he again binds her to him at the end of the Mindflayer Colony - Which is why you have to free her again to be able to harm him.
Seemingly it's something that Ketheric himself did to Aylin (Likely hinted at with the ritual circle in his room, that's seemingly where he studied the ritual required to link his life to another. Presumably after meeting Aylin and finding out that she is immortal)
Of course, the question is how Aylin is so immortal in the first place. Not even Greater Gods can manifest a form that simply shrugs off all injuries like Aylin (And subequently, Ketheric via the binding) seems to do. Like, normally "Immortality" in DnD involves a body "Dying" and then being sent back to a home plane to recuperate for some time. Not just stand there and heal back up like Wolverine/Deadpool.