What happens when one of the pair of conjoined twins dies?

The odds of conjoined twins not sharing at least one vital organ are remote to impossible at best...

i guess that, should it happen, the surviving twin would be given the option for surgery if possible (remember, they still have the right to choose). If necessary, they might be put on some life support to help stop any struggling organs from failing.

If they decline separation, they will likely be made as comfortable as possible until the inevitable death occurs.

Though, in some parts of the world, they could opt for euthanasia and speed up the process.

I know there's a pair that are connected only at the head. They don't share a brain. And of course don't share any vital organs.

I'm guessing they detach the one and try to sew the hole up the best they can.

It is not the same case for all conjoined twins. Some will survive separation, some won't. All would die if left attached to the dead body.

They share one or more of the same vital organs, hence being conjoined. They both die.

They'd probably both die as they share some of their organs