Cloaked Elite chase
Cloaked Elites with plasma swords will chase you for miles. You can test this with the first pair you meet (in the tower) or the subsequent pair that you bump into in the short underpass after the spiral path. They run slightly faster than you, so you'll get a nerve-racking "zzzipppp!" past the ears every several seconds as they go for a swipe with that nasty sword.
What you eventually do with them is up to you. If you're brave, you might try luring one to the drop at the underground bridge, and dodging at the last minute so he falls to his death. For a more explosive send-off, stun the Elite with an overcharge shot from a plasma pistol, then let him have a full clip from a needler. Go on, you know you want to!