So when a player character is downed they start rolling something called a death saving throw. The character is unconscious but still alive and the player rolls a d20 and enough successes they stabilize enough failures they die. A nat 20 you wake up with one health. This is a really good system except the character is out of the fight entirely. It prevents a character from sacrificing himself and ruins some cool roleplay opportunities so I want to present an alternative. I call it the last gasp rule and I've seen variations on it before. The way it works is when a player starts to roll his death saving throws they have the option to instead keep fighting but their character will die. Instead of being knocked unconscious the character receives a mortal wound that they can fight through for four rounds. They have all the abilities and spell slots they had when they fell to 0 hit points and they cannot be knocked down again. At the end of 4 rounds regardless of whether the fight is over they will die. The other characters cannot reverse this except through spells that bring the dead back to life. It gives your players a little additional agency, allows them to really make a difference if they are down to the wire and is really good for roleplay.