Broken power armor
These sets of power armor are so decrepit and battle-worn that they have ceased their primary function of protecting the wearer from harm, though they still provide a bonus to Radiation Resistance - +3 for the helmet, +10 for the armor suit.
A set of broken power armor is found within the Hidden Valley bunker. If you try to take the armor, you will be warned by a member of the Brotherhood of Steel that the item in question still has to be fixed and you will be unable to pick it up. This happens even if you are hidden when you try to take the armor. Therefore, the only way to get the armor and helmet is through console commands or through modded saves.