sunrisekid
Explorer
My players requested that we make the game more "deathy". So we made/stole some house rules, which I copy below. Personally, I still get a bit cringey when characters die, which is common. Note, this is certainly not suitable for all gamers but it's what we do. And, I repeat, players asked for this 
* At 0HP the character is unconscious and finished for the fight (effectively being penalized for poor luck and/or poor decisions)
* At the end of the fight make a single death save: Success = stabilization, failure = dead (this means the character bled out while everyone else was fighting)
Intervention during the fight:
* Heal spells only stabilize the character (who remains at 0HP); the player rolls a death save to regain consciousness and 1HP, otherwise stay unconscious for the fight. Casting a second healing spell works per normal rules (ie, bringing the player back into the fight)
* Use of a healing kit (and Medicine DC10 check if not proficient) gives the dying character an extra death save and a chance to stabilize; failure means you wasted your turn and the character is still dying.
Narratively-speaking, if death saves continue failing until the fight ends it means that the rescuer failed to apply first-aid (but there should be at least 1 death save, if not more granted by someone performing first-aid).
If the character survives then roll on the Lingering Injury table (DMG p272). This injury affects the character until the next adventure, amenable to downtime activities.
(Extra home-brewery note: our campaign does not have gods or clerics. The only healing spell in the game is Cure Wounds, available s usual to other classes.)

* At 0HP the character is unconscious and finished for the fight (effectively being penalized for poor luck and/or poor decisions)
* At the end of the fight make a single death save: Success = stabilization, failure = dead (this means the character bled out while everyone else was fighting)
Intervention during the fight:
* Heal spells only stabilize the character (who remains at 0HP); the player rolls a death save to regain consciousness and 1HP, otherwise stay unconscious for the fight. Casting a second healing spell works per normal rules (ie, bringing the player back into the fight)
* Use of a healing kit (and Medicine DC10 check if not proficient) gives the dying character an extra death save and a chance to stabilize; failure means you wasted your turn and the character is still dying.
Narratively-speaking, if death saves continue failing until the fight ends it means that the rescuer failed to apply first-aid (but there should be at least 1 death save, if not more granted by someone performing first-aid).
If the character survives then roll on the Lingering Injury table (DMG p272). This injury affects the character until the next adventure, amenable to downtime activities.
(Extra home-brewery note: our campaign does not have gods or clerics. The only healing spell in the game is Cure Wounds, available s usual to other classes.)