A Mindbreaker was a non-magician trained to fight and defend with telepathy, though they themselves were not magicians, sorcerers, etc. This allowed them to talk with and shield their minds, as well as look inside others'. It is possible that this term may also apply to magicians that use mental powers, such as Eragon, but it is unlikely, as Eragon states that Mindbreakers are non-magicians. That suggests that telepathic abilities did not require access to the flow of energy one uses to access magic, but simply required concentration.
In theory, anyone could train to defend their mind without being able to break into the minds of others. Nasuada was known to possess this skill and Eragon tutored Roran in it before the battle at Helgrind.