I'm just curious about that the existence of non-rotating stars. Is it physically possible for a star not to rotate at all? Does magnetic braking eventually stop the stellar rotation?
No, this is not possible.
During the stellar formation, some angular momentum will always be present. And any "braking" effects (magnetic, relativistic, tidal etc.) will become weaker as the rotation slows down. So the rotation will never completely stop, because any forces slowing down the rotation will weaken as well.
It is impossible. After the star is "born", it will be rotating because of angular momentum from the place it was formed (most likely a nebula, which is the aftermath of a supernova). Even if there are extremely large amounts of magnetic, tidal, etc. forms of weakening the star's rotation, they will weaken as the star's rotation weakens. The stars rotation could become painfully slow (possibly the slowest speed allowed by the universe), but it is still rotating, just extremely slow.
It's not physically impossible, but it's so improbable that it may as well be so. You would need every tumbling dust grain and swirl of gas to exactly cancel out the rotation of all the other bits of matter that came together to form the star. If that did happen, the most minuscule disturbance would turn it from a non-rotating star into a slowly-rotating star. It's a reasonable assumption that there are no non-rotating stars within the observable universe.