Nearly any time my character gets restrained, they get underwear added. Often the purple lacy bra and panties. Sometimes the black strappy stuff. Why is that? Is there any way to prevent it? I already have the perk free the boobs but I guess that only pertains to chastity devices.

fashionable prisoner perk lets you keep your outfit when jailed

Lore-wise, it’s so you cant hide anything in a more complicated outfit. And it can be an aesthetic preference to keep your prisoners in underwear only :)