The above posters give valuable info on procedures, epecially Scully and Ozzie.
The question, "What happens?" - in reality every dub I have known is so determined to never accept blood that they would be racked with such a terrible bad conscience and guilt that they would confess afterwards
They really believe it would "Displease Jehovah" and cause them to lose everlasting life. They also believe that taking a transfusion is a sure way to get aids, hepatitus or something equally nasty, so they do not see it as life preserving. It is funny how the allowable fractions of the same donated blood do not carry the same risk in their eyes , but there you go.