There is quite common saying, in traditional martial arts schools, when you hurt one of your hands or feet: “you have another hand and two feet, you can still fight!”
In today’s world of health & safety regulations and “better safe than sorry” attitude many people in position of responsibility, like doctors, instructors, teachers or lawyers tend to default toward a safe behaviour when unsure: stop training and rest until healed.
If I followed this rule I would have probably trained about a third of the total time I actually did. When training martial arts (but also other contact sports) injuries do happen, however careful and safe you play. Injuries sometimes occur even during simple drills or exercises, not necessarily during the toughest part of training such as sparring.
Pain exists to remind us that what we are doing is not right for our body and we should really listen to our body; training while ignoring pain could be dangerous and deteriorate the injured part with the risk of causing permanent damages. At the same time there are safe ways of training when injured by using the body parts that don’t hurt so that you keep training them and avoid contact with the injured part.
An extreme case of this behaviour is Alex who recently broke a bone in hit foot by slipping while sparring; although with the foot in a hard cast he kept attending our classes doing stretching, press ups and abdominal exercises so to keep up with fitness and flexibility. At some point as you can see in this video below he was even punching the bag while seated.
In over 30 years of training I was lucky enough to avoid any seriously broken bones (apart from a little toe a couple of years ago) but every time I bruised, mildly dislocated joints or strained muscles on one side of my body I kept training with the other side improving the total symmetry of my techniques.