This is partially a response to the ask from four days ago. I seem to have gradually integrated over time, but I have both personal and second-hand experience with headmate death.
It can be possible to revive a dead headmate, but I cannot give a catch-all method. The requirements for revival can be very simple or very complex, and may depend heavily on both the headmate to be revived and the cause of death. As I cannot provide clear-cut advice, I can offer examples which may help you work out how to revive them.
In one case the headmate originally arrived as a product of hypnosis, and her revival only required the main fronter to hear the trigger word to summon her in order to revive her. However, due to the cause of death - she had committed suicide - she required significant post-revival care to bring her back to a functional state (she was missing a lower arm, was covered in scratches, and was almost completely drained of blood). She made a full physical recovery from this incident.
Another, slightly more complex case involved a headmate of my own; I still feel guilty about what I did. I killed one of my headmates. I was in a particularly foul state of mind at the time and drew her dead in anger, with a chest wound. I thoroughly regretted what I had done, and tried to revive her in many ways. Eventually, erasing the wounds in the original drawing proved successful in reviving her.
The third was more difficult; the headmate of a partner of mine went into a sort of coma after an especially negative, but not directly injuring encounter with another person. Admittedly in a cliche manner she was eventually revived by a heartfelt declaration of love by one of my other headmates (he had been attracted to her for a long time, but hadn’t dared say anything until then).
As for mourning headmates who you truly cannot seem to revive, this is obviously personal, and due to the nature of the world almost always must be low-key; the main idea which I have had was writing the headmate’s name on a piece of paper, tying it to a helium balloon, and releasing it. I suspect however that an act intended to allow the group to move on may make the headmate’s death permanent if it wasn’t before.