Beginning at 14th level, the divine power that fuels your rage allows you to shrug off fatal blows. While raging, having 0 hit points doesn’t knock you unconscious. You still must make death saving throws, and you suffer the normal effects of taking damage while at 0 hit points. However, if you would die due to failing death saving throws, you don’t die until your rage ends.
From the new barbarian Unearthed Arcana. Would the normal rule of being hit while at 0 hp give you automatic death saving throw failures even though you are conscious?