Either no stars pass within a trillion or so kilometers of Sol, in which case nothing interesting happens to the Solar system beyond a few Oort Cloud comets sent Sunward, or else a star DOES pass closely, and it disrupts the orbits of the planets. Worst-case scenario is that a star passes close enough that it completely wrecks planetary orbits, causing them to fall into the Sun or into the interloper, or to be cast out into interstellar space--or worst and rarest of all, the star collides with the Sun, resulting in a small nova that fries the inner planets.