Death saving throws are made on each turn where you are dying and not stable. However, the rules specifically talk about making saves during combat rounds - so what about after combat? Two PCs are up, three are dying, and the lich is defeated. For the three that are dying:
- Do combat turns continue as normal until all are either stable are dead?
- Since combat is over, do the dying PCs make their saves consecutively until they are dead/stable without interference from other PCs? (a combat round in which a save is normally made is only 6 seconds)
- Do the PCs automatically stabilize?
I think the closest interpretation is option 1, but at my home game we've house-ruled to work with option 3 (barring exigent circumstances like a PC dying alone somewhere in a trap) because we assume that in the majority of cases a party can easily stabilize their companion or the PC will make their save.
I'm looking for a rule stating explicitly how death saves work outside of combat, or a wiser interpretation than my own.