What predators have been after Tasmanian tigers and how did they exscape?

The Thylacine (Thylacinus cynocephalus, also known as the Tasmanian Tiger and sometimes the Tasmanian Wolf), became extinct during the 20th century. The last known specimen died in the Hobart Zoo on the 7th of September, 1936. It was a carnivorous marsupial mammal and did not have any natural predators. It was hunted to extinction after a bounty was placed on it as a livestock killer. There is disputed evidence that a very small number may yet still exist in the Tasmanian wilderness, but nobody has seen, photographed or trapped one. A recent attempt was made to clone one, but failed due to the DNA being of insufficient quality.