In 5e rules, when you are down you need to make a death saving throw each round. This is a roll with a difficulty class of 10. If you fail three cumulative saves first, you die. If you make three successful saves first you get back up with 1hp.
Really? I thought that you just stay "downed" when you make three successful saves ...
Or at least that is what mine companions do. :-/
3 Saves and they just keep laying there on the ground waiting for help.