A modder called vagonumero12 dug through the Skyrim code and found out code relevant to haunting and mourning and re-added those lines back to Skyrim.
Here is how both modes were supposed to work in Skyrim according to vagonumero12:
Haunting: when a unique NPC with family dies, there will be a random chance that it will—after some time—”resurrect” as a ghost that will follow a relative for the rest of the game. Only NPCs with generic voice files (don’t expect to see Ulfric as a ghost), and only a single NPC in the whole save. You won’t be able to fill Skyrim with ghosts (it was left like that by Bethesda).Mourning: when a unique NPC with family or friends dies, their relatives/friends will do some comment about their loss to you on their hello dialogues.
Both mechanics don’t appear to have been developed very much before they were cut. Bethesda did however, asked the Skyrim random NPC actors, even those who supplied voices for the children, to record dialogues regarding both mechanics and say things like “my relative died, I’m well sad”.
You can listen to those voice lines here.
You can download the Haunting and Mourning mod here: