Is it permissible for a doctor to draw a small amount of blood that would not harm a patient in a complete and chronic coma, for the purpose of training? And is this considered one of the necessities?

It is not permissible to draw blood from patients for learning and training purposes, even if they are terminally ill, due to the harm and injustice involved. However, if the patient is of sound mind and permits blood to be drawn for the benefit of others, there is no harm in that, provided it does not cause them detriment.