You're getting answers about the asteroid belt because you said asteroids, but I believe your question is about the Oort cloud (comets) since you said surrounding the solar system.
From wikipedia;
> Space probes have yet to reach the area of the Oort cloud. Voyager 1, the fastest[60] and farthest[61][62] of the interplanetary space probes currently leaving the Solar System, will reach the Oort cloud in about 300 years[6][63] and would take about 30,000 years to pass through it.
300 years, huh? I wonder if it'd be prone to Wait Calculation[1] at that level of travel? We'd definitely be dead or well into galaxy exploration by the time it's close to finished with the Oort Cloud.
Either way, I wouldn't be too worried about collisions. To emphasize again, Space is really big and really empty in the grand scheme of things. Outside of a star's gravitation pull, we'd have to be extremely unlucky to have a collision once we get past the planets. And AFAIK there's no signifigant exoplanet within the Oort Cloud.
As for stars: for reference, The Alpha Centauri is the closest to us and that is over twice as far as the edge of the Oort Cloud. It's not like we'd be able to get any data by that point in time, But I imagine crashing into another star outside of our Sun would be a celebrated moment rather than a somber one.
From wikipedia;
> Space probes have yet to reach the area of the Oort cloud. Voyager 1, the fastest[60] and farthest[61][62] of the interplanetary space probes currently leaving the Solar System, will reach the Oort cloud in about 300 years[6][63] and would take about 30,000 years to pass through it.