There are no minor accidents with a chainsaw. And no matter what you do, you can never be 100% safe when you work with them. One slip in judgement and you may have to live with the scars your whole life. Or you won't, in which case you will be dead.
Chainsaws are very dangerous and people who don't know how to work with them shouldn't work with them. Getting training, and learning what can go wrong will never be certain. Every situation is different and when you are out in the wild even a little injury (there are no minor accidents with a chainsaw) can cost you your life.
I wear full protective equipment every time I start one. I look like a total dork, but I don't care.
That means hard hat, chaps, the works.
The chainsaw "chaps" actually will have "strings" of fabric pull out of them that will hopefully clog the sprocket in the saw. While I will admit that having protective clothing that use strings to clog the sprocket sounds a little bit crude, it is effective. These strings will jam the sprocket, and make the clutch slip. The chain stops. In this fashion the pants stop the cutting before the can get through. You may be bruised (in most cases you will be), but you shouldn't get cut.
The helmet with face protection should stop a kickback. And that can be deadly if it strikes you in the shoulder. Training can help here, as it will show you how important body position is.
When cutting, have the saw positioned so if it kicks straight up, it will be to your right-hand side. Instead of cutting in front of you, where it would kick into your face/shoulder. If something bad does happen there is little gurantee that you will escape all injury. Nine times out of ten the answer is, probably not, but if everything goes "right" (there is no right in an accident) you will hopefully be less hurt.
I have seen this first hand, and I can attest to the danger of a saw that is not actively being used. The majority of injuries with a chainsaw happen after the throttle has been released.
Usually taking a step immediately after making a cut.
People have died and lost limbs while engine rpm has been winding down. Most chainsaws rev out to over 13k rpm.
This means that you could easily saw through a 2x4 with a chainsaw after you let go of the throttle. My father made the mistake of letting his guard down and only suffered a tearing cut that ran down the length of his left thigh. The cut was mostly cosmetic so he was one of the lucky ones.
Things could have went very differnt for him.
He was wearing jeans.