Haunting a creature has no inherent rules meaning. It’s a designation that other effects (such as those of Kaya’s emblems) may refer to.
2019-11-12 • wotc
Kaya returns to the battlefield immediately after the creature she haunts leaves the battlefield. When she returns this way, she’s considered a new object and enters with her starting loyalty counters.
2019-11-12 • wotc
If Kaya somehow leaves exile, the creature is no longer haunted. Similarly, if Kaya isn’t exiled by her first ability as it resolves, the creature isn’t haunted.
2019-11-12 • wotc
Kaya’s emblems can target a creature that’s haunted by anything, not just by Kaya.
2019-11-12 • wotc