Can a creature tell when a creature succeeds or fails a death saving throw?

Question

Using nonmagical senses, is it possible to tell:

1. When a creature succeeds (or fails) a death save
2. How many successes/failures a creature has

Answer 1

If they can't, many class abilities are compromised

Death saving throws are one type of saving throw. The game is full of effects that modify saving throws, and sometimes these effects are class abilities that characters can choose to use or not use. For the character to be able to make that choice, they must have knowledge that a save has been made, or is about to be made. Nearly all, if not all, of these abilities require the character making the choice to both be within 30 feet of, and to be able to see, the creature making the save. Most of them do not meet the SAC test for being "magical" abilities. Some examples of such abilities are:

Artificer's Flash of Genius (you know the roll has been made)

Chronurgy Wizard's Chronal Shift (you know whether the save succeeded or failed)

Circle of Stars Druid Cosmic Omen (you know the roll is about to be made)

Divination Wizard's Portent (you know the roll is about to be made)

Oath of the Watchers Paladin's Vigilant Rebuke (you know the save was successful)

Wild Magic Sorcerer's Bend Luck (you know the roll has been made but not the result)

Wish Spell (you know whether the save succeeded or failed)

The existence of these abilities could be taken as evidence that characters have a within-game concept of the 'saving throw', even if they don't call it that, just as they must be able to understand that 1hp is the minimum amount of damage that can exist. It could be that possession of the ability itself is what permits the knowledge about saving throws, and only characters with these abilities have that knowledge. Or it could be that any creature has this knowledge, but only a few have the ability to act on it.

Despite the existence of such abilities, however, the claim that characters do not know "what saving throws are" is popular. If none of the characters in your game have abilities that they can voluntarily use to affect saving throws, then there is no difficulty presented by the DM maintaining that characters do not understand the concept of saving throws.

If, however, some characters do have such an ability, the DM needs to make a decision, at least for those characters. The DM has three choices:

(1) They can maintain that characters don't know what saves are, and thus refuse to allow players to use their characters' class features in the way that they are written.

(2) They can maintain that characters don't know what saves are, but as a DM they will decide when the characters can use these abilities, rather than the players of the characters.

(3) They can maintain that the characters don't know what saves are, but since the players do, the players are permitted to choose when the characters use their abilities. Dale M has called this "if the players know something in the mechanics then the PCs know the equivalent something in the world." That is, there is something the characters are basing their decisions on, even without the concept of 'saving throws'. If one of their downed companions groans and begins rapidly bleeding out (what the character actually might observe), then the player knows that they just failed a death save, and can have the character react accordingly.

To my knowledge, no ability keeps track of, or interacts differently based on, the number of successful and failed death saves. Making this number public knowledge, at least for the PCs, is practiced at many tables, though.

Further reading: Is there a way to force a reroll on a saving throw?

Do reactions that trigger on saving throws give knowledge of saving throws that would otherwise be secret?

Do characters know if someone else, who they can see, has failed a saving throw?

Answer 2

The rules don't say

The section about Death Saving Throws (p. 197) does not make any statement on it. However making death saves is

to determine whether you creep closer to death or hang onto life.

while the creature is Unconscious. There is likely no external, easily observable sign that would tell other characters how close the creature is to actually dying, at least not without something like a Wisdom (Medicine) check.

This is a little awkward, because it is the player that makes the saving throws:

Whenever you start your turn with 0 hit points, you must make a special saving throw

and most tables I know roll saves openly, so all the players have full knowledge of how things look, even if their characters do not. That poses a challenge of not letting yourself be influenced by that knowledge when making tactical combat decisions for your character. How you handle it is up to your table, but in my experience, players will rightfully begrudge it if you tried to penalize them from pulling all the stops to stabilize or heal their fellow that is at two failed death saves, just because their characters would not know.