They don't. Proxima Centauri is 4.2 lightyears away and is our nearest neighbor. There is enough distance for another star to pass between us without seriously disturbing either system. In order for a stable system to decay into a collision, a third object would have to be involved. Or the colliding object could be a runaway star, possibly liberated when another multiple system broke down.
Interestingly, the study of mass extinctions led to the belief that we've suffered massive comet impacts about every 27,000,000 years. This could happen if we had an undetected binary star and it's orbit dislodged objects from the Kuiper Belt at this interval. Some astronomers are taking the suggestion seriously enough to look for the object. And if there are two massive objects circling the solar system, we may be screwed. :)
It occurs to me that you could dislodge 10,000 comets and send them toward the sun and the likelihood of a direct impact on Earth would still be statistically unlikely. Thus, for the "every 27,000,000 years" theory to hold up mathematically, a truly dizzying number of objects would have to be sent in.