Encroachment cycling prevents a player from being damaged by repeatedly encroaching (blocking) a mover.
In some Unreal servers (Zombie's Deadzone), the player is damaged for repeatedly blocking a mover. Say, if a player stands under a lift and prevents the lift from reaching the ground, it will strike the player and deal damage to them. Damage is only given after the player encroaches the mover several times. Encroachment cycling is the tactic of encroaching a different mover every time. Because there appears to be a single variable containing only the last mover encroached & an associated "number of times the player blocked a mover," if the player never blocks the same mover twice in a row, they will never receive damage.
This tactic would be useful in maps where the player can encroach multiple movers in close proximity, avoiding damage altogether to enact an active block.