I've heard plenty of debates on this issue. But considering the vast amounts of dead space involved, there's actually very little likelihood that we'd be one of the things anything would collide with. Considering the life on earth probably won't live that long, we won't be affected by this event when it does happen. But if it happened tomorrow, there's so much space between everything, you'd hardly notice if another star came between us and alpha centauri. The odds are surprisingly good. Galaxies may look dense and have billions of stars. But that's in a range of hundreds of thousands of lightyears. One analogy I heard was that if the sun was the size of the tip of a pin, then the galaxy would be the size of america. Another analogy I heard was that if the sun were the size of a baseball, then the next closest star would be in texas. Which is MORE than enough space for a star (or dozens) to fall through without hurting much

Granted gravity and orbits might be skewed a bit. The galaxy as a whole would definitely be impacted. But the planets that would orbit those stars would still be stuck to those stars. Worst case scenario is the dust clouds on the outer reaches of the star's gravitational pull get interrupted and start hailing meteors and comets into the solar system again