The "Living Death" was caused by one of the major Sebacean weaknesses, their vulnerability to heat. Being exposed to too much heat could cause heat delirium, which was the first stage of the Living Death. It was a state where all higher brain functions were shut down and only the body lived on.
Aeryn Sun had a close encounter with Living Death, but was brought back before it could occur. ("Exodus From Genesis")
A few cycles later, Aeryn was in a similar far-progressed state of heat delirium (only not naturally caused, this was by a highly advanced virus created by beings who wanted her to stand on trial), but Scorpius saved her by giving her a similar cooling suit as he. ("Promises")