If you are experiencing this ce-34878-0 error code, please close the application and then install the latest system software and game patch.If the error occurs again, initialise the PS4 system after back-up of the save data and please also submit any crash reports after re-booting your console when the error occurs.
[PlayStation Forum, Via IGN]
A number of PlayStation 4 users have reported a system error that resulted in corrupted save files, nullifying hours of hard-earned in-game progress.
Gamers have lamented the issue over on the PlayStation forums, citing the issue as Error CE-34878-0. One Joystiq reader told the outlet that he lost a whopping 30 hours of progress. That's rough.
Users have reported the issue occurring for the following games: Assassin's Creed IV: Black Flag, NBA 2K14, Call of Duty: Ghosts, and Battlefield 4. There are even select cases in which some gamers have said the error won't let them open any applications on the system at all, which is obviously quite problematic.
Sony is likely on the issue, so hopefully we'll have news of a fix very soon.