If this is not the kind of active position you are looking for, try this instead: active.
Active position is a term coined by Bill Spight in analogy to Hyperactive Position.
The value of a play in an active position depends upon who is komaster, even though the count remains the same.
Typically such positions are sente, but who can win the related ko or kos determines the size of the reverse sente play.
Bill: The reason that there is no example is that active positions are rare. (I have no files named to indicate an active position, though there are probably two or three that contain one.) One way that they can arise is with a sente ko (where taking the ko is sente) when the value of the resulting position after the reverse sente depends upon who is komaster.