Actions while incapacitated

[Anth]

If there is a fight and the rogue in the party sees an interesting door and goes looting.
After a while he comes back to the fight and I would rule the he has to reroll his initiative - because has no idea what happend during the time he was gone.
(I can understand those that keep his initiative for simplicity reasons)
I see no difference between an uncouncious fighter and a person that leaves the room and then enter.

 

[Taren Seeker]

If there is a fight and the rogue in the party sees an interesting door and goes looting.
After a while he comes back to the fight and I would rule the he has to reroll his initiative - because has no idea what happend during the time he was gone.
(I can understand those that keep his initiative for simplicity reasons)
I see no difference between an uncouncious fighter and a person that leaves the room and then enter.

The PC is still involved in the combat. If he's knocked out for a certain number of rounds, the effect counts down. If he's bleeding out, he still makes stabilization checks on his turn. When he wakes up, he acts on the same turn he always had.

BTW, in your example if the rogue is aware of the combat, he enters at the top of the initiative order. I think it's stated in the DMG.