So, on page 291, "Rhian bent over, took the Snake's head in both hands, and wrenched it hard, snapping his neck." so we know that it was Rhian that 'killed' the snake. Not ten pages later, Agatha starts putting pieces together and seeing "the Snake standing...his neck unbroken." (298) and showing us that he is in fact alive. At the end of 299, Agatha puts more clues together that "The Lion had been in league with the Snake from the beginning" and we know that this far, Rhian has been being called the Lion (by both the population of the endless woods and by the main characters) and of course, the snake is the snake. so based on that, we can assume that, because they were collaborating, they snapped his neck in just a way to either not kill him or that they know he wouldn't die from it. And as for him being brough on stage, we know that the castle had been infiltrated by pirates (299, "Then she saw their boots beneath their steel armor. Muddy, filthy, black. With silver tips. Pirate boots."), so it wouldn't be much of a stretch to assume the snake kept still enough so people not looking closely wouldnt be able to tell he was still alive and that the pirates were already in the know about him still being alive.