The Jedi statues of the Sith were always motionless and steady, as with the temple's Sith statues, and held a lightsaber. Created as guardians against intruders, their stone bodies were animated by the Force when trespassers got too near, presumably through some sort of Sith magic. On alien presence, the lightsaber was ignited and they came to life like stone automatons to fight the intruder.
Any non-lightsaber wielder who met them was doomed since the Dark Force aura of the planet meddled with all mechanical weapons except lightsabers.
Behind the scenes
While the name Sith Jedi seems awkward, being an oxymoron, this is the production name of the enemy unit in the Mysteries of the Sith official site. There is not enough information on their origins or nature to challenge its naming.
- Jedi Knight: Mysteries of the Sith game manual