OK, so I have this super elaborate headcanon about what happens to Clara and Ashildr, and it goes thus:
After a few years of traveling, Clara checks her pulse and finds she has a heartbeat. At first, she and Ashildr just assume that they’ve gone out of Gallifrey’s reach or something. But then Ashildr checks her DNA to see if she’s aging, and the TARDIS says she’s a Time Lady.
They both travel to Gallifrey to ask the Time Lords for help, and they explain that Time Lords evolved by living around Time energy, which affected their DNA. Humans are not effected by Time Energy because their cells keep renewing, keeping them human. But because Clara’s cells do not renew since she is frozen in time, the Time Energy in the TARDIS gradually turns her into a Time Lady, complete with two hearts and 12 regeneration’s. The reason she can hear her heart is that Time Lord death occurs on when both hearts stop beating, and Clara’s second heart is still going, while her first heart is frozen.
Because of this, Clara goes out to face the raven. It kills her, and she lies motionless. After the Doctor her in a room, Clara leaves a note for Rigsy telling him not to tell anyone and even paint the Doctor’s TARDIS as a memorial to her to make her death look real, and Clara sneaks away to her TARDIS. Like Jenny (the doctor’s daughter, look it up if you don’t know) she regenerates into another body of herself.
With no fear of damaging the universe, Clara and Ashildr carry on traveling.