They retain the passive, not the active of their former race.
No, the demonstration showed they still retain the active.
Fane had Encourage.
Actually, if you check again the Undead reveal stream, they start with an Undead lizard, his active is play dead, he doesn't have the lizard active.
Don't forget that icon don't get removed as you lose memory of change form. So you would get the icon of encourage even when switching to something else, even if you can't use it anymore.
So I still think you only get one active.
In the undead stream the icons did change from play dead to metamorphose when they used the shapeshifting mask to change from undead to dwarf, so I don't think that explains the errant encourage.
But, based on the character creation shown on that same stream I think it is correct that an undead character has the active skill of the race replaced with play dead.
As for Fane having encourage in the stream, there are some possibilities for why: (1) It was a bug (2) he was wearing an item that granted the skill, like the teleport gloves in the EA, (3) he had the shape shifting mask, changed into an elf, as an elf ate something that gave him the skill, then shifted back to his undead form.