I was thinking about the impending collision between M31 and the milky way galaxy, and I've heard that since a galaxy is mostly space most of the contents of both galaxies would be just fine. Could a similar effect be responsible for the late heavy bombardment era? Just instead of galaxies, stellar systems?
There are several potential explanation for the cause of the late heavy bombardment. One of them includes a passing star that disturbed the Oort cloud. A "stellar system collision" would have destroyed the solar system, though. While galaxies are mostly empty and a galactic collision won't involve that many actual collisions (if any), the gravitational interactions between the galaxies actually changes star orbits around the galactic centers. Similarly a "stellar system collision" would heavily change planetary orbits, even if there were no collisions at first.
Another hypothesis is a totally "interior" one: A 2:1 orbital resonance between Jupiter and Saturn changed the orbits of Neptune and Uranus, potentially even causing them to swap positions. Neptune's new orbit then affected many Kuiper belt objects, either sending them way out to form or join the Oort cloud, or sending them in as part of the late heavy bombardment.