Since Clara stepped into the Doctors timestream, and already exists in pretty much every part of it, she isn't like most humans. The point is, doesn't this connection give her something that would allow her to survive the thing that would have caused Donna to burn up, had the Doctor not wiped her mind? Mightn't a "Doctor Clara" be possible?
Think... Doc is mortally wounded, and needs to regenerate, but isn't sure how many, if any, regenerations he might have left. Fearing he might not have enough energy for a full regeneration, he reaches out to Clara, who is also wounded, and might not survive without a miracle. And the Doctor kinda saves both of them, by redirecting his regeneration energy into Clara. He has just enough regeneration energy to repair her wounds, and to fully integrate their minds. She awakes, with "The Doctor" fully integrated into her own mind, which is now also fully aware of its various incarnations as The Impossible Girl. She becomes the Doctor, and is still, in a sense, the REAL Doctor, as he is now a very real part of her. (Maybe the integration isn't perfect, so she can get into an occasional humorous argument with herself?)