There is a general rule that if you have an injury or sickness you stop training until you've recovered. However Soke Hatsumi has said "When weak or injured always continue training as you should always be able to adapt in any condition". So how do we reconcile these two views?
The best answer is unsurprisingly by the application of that rare super power common sense. To stop training when injured or sick causes a few issues. First of all it can affect the confidence and enthusiasm of a student - I have an injury now, will it happen again, how will I be received when I return, do I want to risk it again? Another issue is with how it affects the level a student is at. They can feel they go back a step with an absence from training with physical skill and understanding. The other big disadvantage is a more practical one - how will you defend yourself if you are injured or sick? If you don't look at this issue you are actually creating a weakness or flaw in your abilities, where you loose confidence in your abilities when injured or feeling under the weather.
With all that said, how do we train in an effective and safe manner when ill or injured? Well lets start with the fact that not all training is physical. It is a common misconception that when we say 'training' people tend to think of punching and kicking bags (and people). For those engaged in traditional arts there is a significant amount of philosophy and academic study that is a part of the art. Even those that have a purely competition focus in their training, time is always well spent studying the opponents competitions, strategies and different styles.
Physical training can carry on with physical injuries - you need to adapt your movement to protect the injury. If you have a fractured hand you need to change the movements to adapt to protect this - so hit with the other hand, kick instead of punching, throw instead of striking. Pain can affect not only the injured part but also your posture, your dynamic movements and your focus. It is a good idea to find out how you as an individual will react to this, as in a fight it is very rare to come away uninjured.
It is difficult to advise on a blog what you should do specifically but the principle is in adaptability. If you feel your injury or ailment is too severe to train with then at least be present at training to watch. This way you will get a sense of what is being taught and keep the contact with those involved.
To end with another Soke Hatsumi quote "Keep going". Ninjutsu is a life long study, and there is only so much life in us all.