Ends: Following a cutscene after you run from him for about two rooms.

Does the Tyrant ever stop chasing you?

You can't eliminate the Tyrant. ... The Tyrant will also chase Leon while he is in the Nest (Umbrella's laboratory). However, he will do that only for a moment - he stops chasing Leon after he finds the wristband that gives him level III permission.

Does the Tyrant chase Claire?

He appears in the main story after dousing the flaming helicopter, and will pursue you until you leave the Police Station Parking Garage. ... In Claire's Story, he will appear in the Parking Garage once you insert the Key Card, and chase you until you pass through the gate knocked down by the zombies on the street.