I recently watched the documentary Tukdam: Between Worlds. This explored the phenomenon in Tibetan Buddhism where experienced practitioners can remain in a state of meditation after the body has shown all physical signs of having died - no breathing, the heart has stopped. In this state the body can support itself, the skin looks healthy, there is no sign of decomposition of the body (even in the heat of India where many of the exiled Tibetan community now live), and a feeling of warmth remains around the heart. This can last for days and sometimes weeks.
With the support of His Holiness the Dalai Lama, scientists have started examining those who are in this state, trying to understand what is going on. So far, they have few conclusions it seems, other than an acknowledgment that this phenomenon is happening.
There is skepticism in some circles as to whether western science is capable of measuring anything while practitioners remain in this state. Their argument is that consciousness is not material, from a Tibetan Buddhist perspective, and so is beyond the measurement of modern scientific instruments.
Be that as it may, His Holiness the Dalai Lama appears keen that the investigations continues, even if it does take a long time to come to conclusions.
Here is a preview of the documentary.