What if you could hold your ground?

Imagine that you had an interesting quality that makes it impossible for anyone to move you against your will. Furthermore, along with your ability to demobilize yourself you would necessarily be invulnerable, and very strong. Noone could withstand a sustained conflict against you.

What would happen if a person had these qualities and decided they would hold their ground. Would civilization be able to ignore this geographical point, or lose it. How much would the location of the stand off impact the world.