Ok here is an example from an actual game. I will explain the problems and how they solved them.
The units:
Horse Archer beat Infantry and Heavy Cavalry but are beaten by Archers
Infantry beat Heavy Cavalry adn are beaten by Horse Archers and Archers
Heavy Cavalry beat Archers but are beaten by Horse Archers and Infantry
Archers beat Horse Archers and Infantry and are beaten by Heavy Cavalry
As it stands in this game Infantry are next to usless. There would be no situation where you had other units and needed Infantry.
The designer fixed this by createing a system where, during combat a unit had to either give ground or take ground. He then decided to allow the special ability of infantry to be that they were then only one that could hold ground in combat, providing a defensive units to maintian control of territories. This gives it an ability that is useful in certain circumstances where the other units would not work.
This nesessitated changes to the mechanics and rules to impliment.
A game where this unit dominance system exists (without the fix) is the computer game "Age of Empires". The designers included the infantry unit but the resource mecanics meant that holding ground was not needed. The infantry unit was not used, even when the designers halved (and that is a big change) the cost of infantry it was still not worth using.
So the examples that I listed were to demonstrate that having certain paterns of dominance of choices over others can healp break the "game on autopilot" syndrome, by giving players a choice that will effect their position in meaningful ways (give them an interesting chioce). Of course this is not the only way to do it, and not the only aspect to consider. It is only 1 tool in the toolbox of game design.