What house rules did you put in place?
At the time we used them:
1. Going to 0 HP gave you a level of exhaustion.
2. Rolling for Lingering Injuries (DMG pg. 272) when at 0 HP.
3. You must be restored to at least 5 HP before you regain consciousness.
4. (
EDITED before I forgot it before) Your death save failures do not reset until you finish a short rest or your current hit points are at least half your maximum hit points.
Results of these changes:
1. People wanted healing or to break away from combat if they got close to 0 at all. No one wanted a level of exhaustion due to the death spiral effect of accumulating levels. Others didn't want you to get them, either, because you were less effective, required spells or more rest to restore you, and such.
2. Most of the time this was an annoyance, but once in a while you got something bad and it became more of an issue in play. When players saw this happen a couple times, they grew to respect the possibility more and avoid going to 0 HP more.
3. No more feeding the downed PC a
goodberry to get them conscious again. Sometimes even a healing potion wouldn't be enough. So, it cost greater resources (slightly) to get you back into the fight.
Admittedly, #1 is the biggest and that alone encourages more cautious play and combats. You go down, get up, go down, get up, go down again... and suddenly you have three levels of exhaustion: half speed and disadvantage on ability checks, attack rolls,
and saving throws! That is pretty brutal really. AND it lasts and takes time to remove (or powerful magic).
There are other rules we've used to make the game more deadly as well:
1. Death saves are a DC 15 Constitution check. (Not a save, a check, so no proficiency bonus except for Jack of All Trades and Remarkable Athlete.)
2. Death save successes and failures cancel out until three successes or three failures are reached.
3. Each time you die, you gain a permanent death save failure. (In other words, you can start with 1 or 2 death save failures when you go to 0 HP!) This means the 3rd time you die, you are
forever dead, short of a
Wish spell or such to remove on of the permanent death save failures.
Results of these changes:
1. You are unlikely to stabilize on your own. Someone will need to help you.
2. It won't be decided in five rounds or less. We had a PC seesaw back and forth between success and failure for over 10 rounds before.
3. If you've died once, your tie to life is weaker and you are more likely to die again. Also, no more infinite lives. Basically, you die three times and you're out.
Parts might seem harsh, but yeah, no more whack-a-mole at our table.
Players are more cautious about entering combat in general and there is more talking/ negotiations than before as a result.