As the stars are squeezed into the "narrow" paths, the density will rise sharply and ultimately these will give rise to a black hole, near the centre of the galaxy.
CL,
We cannot compare the Solar System (or other solar systems) with the Milkyway (or other galaxies) in this way.
The Saturn Rings system is more close to the galaxies as far as motions are concerned.
This was pointed out by Frank Hsu.