Hero Statues are objects that villains can destroy during the mission Destroy statues in Steel Canyon from Operative Wellman. There are two of them, have the same Hit Points than a Boss of the same level and no defenses, nor they are able to move. There will be three Wyvern Sting agents guarding each of them, though.
These objects are also found during the cape missions from Mr. Rodney, Kalinda, and Matthew Burke, guarded by Longbow agents. Once the first statue is destroyed, an ambush is spawned. When the final statue is destroyed, another ambush is spawned, followed by a final ambush containing the target hero being spawned to attack you.
They have a faction of "Relic", and have been observed to have three different models of statues, but they all share the same Hit Points and powers (or lack of them).
There's a known bug that allows the statues to change facing and turn around for some reason.