"stabilize shape" means "make the stars orbit the galaxy center at the observed velocity".
You would expect the stars closest to the center to orbit with a higher angular velocity than those farther out, but this is not exactly what is being observed in reality. The hypothesis is that there is invisible, non colliding, yet gravitating, "dark" matter which skews the mass distribution in such a way that the observed orbit velocities again make sense.
This means that the "dots" can equally well destabilize the simulation, since they are essentially just gravitating bodies... invisible stars.