MarkB
Legend
I do agree that players making the stabilisation roll on their turn can have a somewhat unfair effect under certain circumstances.
I don't agree that using the Delay action is the way to deal with it.
If you want to make things fairer, combine your solution with the house rule your player suggsted: When a player drops due to hitpoint loss, reset their initiative to the count on which they dropped, and have them start making stabilisation rolls from the next round. That way you get the best of both worlds - further hitpoint loss always occurs exactly a round after the damage was inflicted, and it occurs on the character's initiative so you don't risk accidentally skipping it.
I don't agree that using the Delay action is the way to deal with it.
If you want to make things fairer, combine your solution with the house rule your player suggsted: When a player drops due to hitpoint loss, reset their initiative to the count on which they dropped, and have them start making stabilisation rolls from the next round. That way you get the best of both worlds - further hitpoint loss always occurs exactly a round after the damage was inflicted, and it occurs on the character's initiative so you don't risk accidentally skipping it.