Question: How much damage would a space probe cause if it can get about 4 lightyears away in 10 years and doesn't have any brakes when it arrives? Could it cause a global extinction event on the planet it was sent to? Do actual concept probes think about this?

Answer: 
Let's assume it travels at a constant speed of .4c (since we don't know anything about its acceleration) and its mass is 100kg. At those speeds, the relativistic effects are minor compared to the fact that I just totally made the mass up out of thin air, so we can do a classical solution.

Using $E=1/2mv^2$ we find that the energy is $1/2 \times 100 \times 119916983^2 = 7.19004143 \times 10^{17} ~\mathrm J$. Using my favorite page on the internet, [Orders of Magnitude (Energy)](https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)), we see that that's on par with detonating the Tsar Bomba, the largest nuclear weapon ever built. It's 6 orders of magnitude off from the energy released by the Chicxulub meteor event that is believed to have caused the extinction of the dinosaurs.

Thus there's little risk of an extinction event. That and hitting a planet by accident 4 light years away without trying is pretty hard!
First of all, even without an artificial braking system, a spaceship can slow down using tidal forces of the planets/astronomical bodies it passes by, just as it can speed up using gravitational assist. So, it will not necessarily reach cataclysmic speeds simply by travelling for a long time through space.

Now, let's estimate the energy that will be released if the space probe *[New Horizons](https://en.wikipedia.org/wiki/New_Horizons)* crashed into a planet like earth. *New Horizon* has a gross weight of about 400 kg. Its last recorded speed (the world record currently) is 16.26 km/s = 16260 m/s. Let's assume it crashes with this speed. And all of its kinetic energy is converted into heat. The heat released will be about 53,000,000,000 J. A ton of TNT produces about 4.184 $\*$ $10^9$ J of energy. The energy released in the crash event is about 10 times this energy. That's about enough to blow a large enough tunnel in an average mountain. The planet won't even notice.