Clerical healing should recompose the body of the decayed undead. Skeletons, zombies, ghouls, wights, mummies, liches all take damage from cure light wounds, cure serious wounds and heal. Higher-level undead such as liches would get a saving throw against healing. Mummies too, if you think that’s reasonable. I don’t count vampires in this at all, but you can if you want.
If an undead is healed an amount equal to its HP, the body is completely recomposed and the spirit is briefly recalled to the body in order to die again. If it helps the adventure or mood, the dearly unparted might have time to say something brief on the way back out.
I can think of one way this might be useful. One of my favorite deities posted here is Owrox, who abducts souls for ransom. If a magic user were to animate a body, then a cleric heal it back, the soul would be recalled briefly. If if could be directed to its proper destination somehow, that would allow escape from Owrox or some similar demon. And it just might work. Once.
The enmity of a soul-stealer would be a tremendous burden for anyone who tried such a thing. And of course how would you ever find a cleric and a mage in the same party of people? Someone would have to be awfully rich to do such a thing…
Note: I have no idea if this is already in place in more recent editions. If so, well it wouldn’t be the first time. I’m playing in my first game of post 1e D&D in a few weeks, in a Pathfinder mini-campaign.
Also, this is post 100.