"Safe" is such a relative term. Playing paddy-cake in a padded room could be unsafe to certain individuals, I'm sure. Really, it all depends on your definition of "safe". Are you going to die from jiu jitsu? No. Well... actually, the possibility is there, but you have a better chance of dying from a lightning strike.
Dying aside, let's get one thing straight: Brazilian jiu jitsu is a martial (i.e. "fighting") art. As such, there's an unavoidable element of risk and potential for injury. Here's what you can expect:
- You will get bruises, especially when you first start out and your body hasn't adjusted to the forceful grabbing by your opponent or the innumerable impacts of someone's elbows, knees and other random body parts. Don't worry, your body quickly adjusts and you'll stop bruising so easily after a month or two. If it doesn't, make sure you're getting enough vitamins in your diet.
- You will get the occasional black eye from a stray knee, elbow or accidental headbutt. It happens. When you have two people rolling around on the floor, both trying to obtain a more dominant position and often moving in wild and unpredictable ways, odds are your face is going to get in the way. It may or may not result in a full-blown shiner, but you will get some discoloration. Concealer comes in handy if you're worried about going out in public.
- You will roll your ankle or strain some other ligament sometime during your career. If you don't, you've got some serous Luck O' the Irish on your side. Again, you and your opponent are moving around in sometimes unpredictable ways, so it will happen that you'll plant your foot or hand in an unstable position, allowing for the possibility that it will be rolled or twisted. When it happens, stop the roll, assess the damage, wipe away your crocodile tears and get it taken care of.
- You may break something. Considering how many people are practicing the gentle art around the world, actually breaking something is exceedingly rare. It does happen, but this is either due to an extreme - and freak - accident, or because you didn't tap when you should have. Again, jiu jitsu is a martial art. The risk of breaking something is far higher when you're engaged in a fighting discipline, than when you're sitting on the couch watching television. Just get into the habit of tapping early and tapping often.
Again, whether or not jiu jitsu is "safe" really depends on your definition of the word. If you're looking for a hobby or sport in which you won't have to worry about breaking a nail, you should probably look elsewhere. If you're looking for something that's combative but you don't want to be punched in the face on the daily, jiu jitsu is going to be that "safe" alternative.
The beauty of Brazilian jiu jitsu is that you can always tap. Unless you're paired with a real disaster of a human being, everyone you train with will respect the tap. If you feel pain or you're unable to breathe, just tap.
Train on... safely. Oss.