What Happens?

NOTHING!

The stars in galaxies are so spread out that the chances of stellar collisions are practically zero. During a typical galaxy collision, only a few pairs of stars will collide. The odds that planets collide are even smaller.

Planetary systems are at a bit more risk, because a star moving through can disrupt planetary orbits even if it doesn't hit anything. But the chances of this happening during a galaxy collision are not much greater than they are at other times.