If you're familiar at all with Doctor Who you could design a D&D version of the Weeping Angel (at least I think that's what they're called) - angelic statue-like creatures that cannot move if somebody is looking at them but can move if nobody sees.
Lanefan
All you'd really need to do is create a "stage" for the creature where it has low AC, and cannot act, but has a high DR. Then just apply it to whatever creature you want to be the statue.
This is the PRO TIP answer. You don't need different stats, just different skins.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.