I've been assuming that granting death saving throws was probably not a good thing, but this recent question got me thinking.
Death saving throws are a type of saving throw, so you should be able to grant saves versus the dying condition.
You can't take actions when you are dying, but I looked at several powers that grant saving throws, and none of them specify that the character rolling the save will need to use an action. Example:
Divine Aid, Cleric Utility 2
Standard Action, Ranged 5
Target: You or one ally
Effect: The target makes a saving throw with a bonus equal to your Charisma modifier
However, the Dying and Death section of the Rules Compendium states that if you roll 9 or lower on a death saving throw, then "The adventurer slips one step closer to death. If this result comes up three times before the adventurer takes a short or extended rest, he or she dies."
Can you grant additional death saving throws to a dying character?
If so, would a failed saving throw granted by a power like Divine Aid count towards the failed death save total, potentially leading to the adventurer dying sooner?