A quick read over the suffocation rules for 5E (see p.183 in the PHB) gives this snippet of text:
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.
So, after dropping to 0HP, the creature begins making Death Saving Throws as normal. But here's my question...can they stabilize? Per the RAW, it seems like they should be able to stabilize and stop dying, despite the fact that they did not reacquire access to oxygen...but that doesn't make sense. Am I missing something?
The way I'd personally rule it is that 3 'successful' saving throws resets the Death Save, clearing your failures back to zero, allowing you to stay alive longer...but you can't stabilize while you are still suffocating. But I'd like to know if there's anything like an official interpretation that makes sense.