I notice that a lot of characters have a belted tunic in their inventory, yet they never equip it.

You can pickpocket them off and they magically have another one a while later.

I pickpocketed Karlina and Brynof's belted tunic a second before they activate the nightingale armor stones. As soon as the nightingale armor is equipped, they have another set of belted tunics.

Why?

Belted tunics are the life force of every living thing in Tamriel.

Belted Tunics are basically the equivalent of a briar for a briarheart.

Don't trust anyone in a Tunic.......