DAYUM!
I’m thinking a tumor-causing virus carried in the saliva.
http://www.britannica.com/animal/Tasmanian-devil
Tasmanian devils are related to quolls (catlike Australian marsupials, also called native cats); both are classified in the family Dasyuridae. The teeth and jaws of Tasmanian devils are in many respects developed like those of a hyena. The pouch, when relaxed, opens backward, but, when the muscles are contracted to close it, the opening is central. During the breeding season, 20 or more eggs may be released, but most of these fail to develop. In most cases just four young are produced after a gestation period of about three weeks; these remain in the pouch for about five months. Overall, female offspring outnumber males about two to one...
...The Tasmanian devil’s immune system does not recognize the cancer cells as foreign and therefore does not attempt to kill them.