If this is possible, it allows an exploit: destabilize, wait for death save.
- Success -> wait another turn
- Failure/Critical Failure -> Cleric casts Spare the Dying, then destabilize again
- Critical Success -> Character is awake at 1 hp
If this is possible, it allows an exploit: destabilize, wait for death save.
PHB, p. 197
Stabilizing a Creature
A stable creature doesn’t make death saving throws, even though it has 0 hit points, but it does remain unconscious. The creature stops being stable, and must start making death saving throws again, if it takes any damage.
So the only way to stop a creature from being stable is to deal damage to it. (Or, to heal it, but then it is not going from stable to not stable at 0 hits). However, there is also this rule
Damage at 0 Hit Points. If you take any damage while you have 0 hit points, you suffer a death saving throw failure.
So you can stop them from being stable, but not without them failing a death save. (Thanks to @DarthPseudonym for pointing out that last part.)
There is the rule for suffocating which says
When a creature runs out of breath, it can survive for a number of rounds equal to its Constitution modifier (minimum 1 round). At the start of its next turn, it drops to 0 hit points and is dying.
While it is not clear if you can "drop" from 0 hit points to 0 hit points, if you could not, being unconscious and stable would make you immune to suffocation, which cannot be the way this works.
Assuming you can tell if a creature is dying or not, suffocating takes minutes:
A creature can hold its breath for a number of minutes equal to 1 + its Constitution modifier (minimum of 30 seconds).
So each try will take you typically a minute or more (few characters opt to have a negative modifier on Con). You can expect a critical success only one in 20 times. So on average, at best you can expect this to take a little more than 20 minutes, instead of the 1d4 hours it normally would take to regain a hit point.