The problem with most sets of conjoined twins is the sharing of limbs, internal or external organs, or blood supply, which usually means the death of one or both after separation.internal. Even in the case of conkoined twins dying of natrual causes, as occured with the original Siamese twins Chang and Eng Bunker, who were joined at the chest, the death of one caused terrible distress to the other, who died a few hours later. The Tehran sisters are aware that one, probably both of them will die, but they feel it is a risk they are prepare to take.